You do not. You rewire. It is 2022, and all 220 appliances require a 4 wire 220 circuit. They specifically cannot be plugged into a GFI outlet. 2 wire is ancient ancient ancient unsafe history.

@Verbo Many of the Chinese induction cooktops sold on Amazon come with two wires. You could not even do a three-wire install if you wanted to.

Set code issues aside for a moment, and I can contact my city to get their rules. My question was whether a two-wire 220V appliance could be connected to GFCI. I gather that this would require you to convert the hard-wire appliance into a 220V screw-lock 220V plug and then attach that into the appropriate 220V GFCI receptacle? But that would violate its own set of codes since a 220V appliance is supposed to be hard wired?

Nobody does GFCI inline to a hardwired circuit?

It's not a matter of "no longer" here. This situation was never legal (well not in anything approximating a modern version of the code). What used to be allowed was to use the grounded conductor (i.e., the neutral/white wire) as the equipment grounding conductor and still is under certain circumstances.

Are you sure there is no ground? Is this box fed by armored cable or conduit?

I wonder is there is not some confusion among the comments here. Certainly there are appliances that use ONLY 240 Vac connections, without the neutral. Otherwise NEMA L6 and 6 plugs and receptacles would be in violation. Note that these circuits also need to be grounded.

From the appliance point of view, the ground should be via a green insulated or bare copper conductor, but may be carried via armored conduit (raceway).

Note that the other appliance conductors may require connection using devices temperature rated the same as the appliance conductors. This is a typical reason for hard wiring, because wire nuts and certain other devices are rated to 110C, and most plugs and receptacles only to 90C.

The OP needs to determine the current requirement of the cooktop, needs to ensure that the conductors from box to cooktop are capable under the usual conditions of that current, and that there is a breaker protecting those conductors rated for that current. Then, to achieve GFCI, that breaker has to be replaced by one that is suitable for the box, or more precisely, acceptable to the local electrical code enforcement officer, who has final authority. How does the OP know that there are not modern breakers that fit his breaker box?

This entire subject just begs for involvement of an electrician who will know all this stuff -- one hopes.

To the OP, if something is shorted, an old non-GFCI breaker (if functional) will open the circuit. GFCI breakers are to protect humans from cases where there is leakage to some part one can come into contact with. Combo breakers (GFCI + AFCI) also detect arcing that might not be sufficient to otherwise cause a current overlord. These are mainly useful against house wiring subject to nail penetration in walls, and zip cords that are under rugs or otherwise subject to damage.

If the feed to the box does not have a grounding conductor, then for use where the appliance does not need a neutral, the white neutral conductor can be re-purposed at the appliance box and at the breaker box by using it as a grounding conductor. Green tape will be needed to reveal that to future electricians.

Last, let me observe for the OP that the drawing is defective and hence misleading. A cable is not a conduit and has to contain a grounding conductor that terminates in the box where the cooktop flex terminates. The flex, box, and grounding conductor have to be in good electrical contact.

"I wonder is there is not some confusion among the comments here. Certainly there are appliances that use ONLY 240 Vac connections, without the neutral. Otherwise NEMA L6 and 6 plugs and receptacles would be in violation. Note that these circuits also need to be grounded."

Yes, this seems to be exactly what is happening. If you want to put a receptical for a car charger or a welder in your garage you must now wire a NEMA 14-50 120/240V receptacle and may not use a NEMA 6-50 240V receptacle (for example), even though the car is a pure 240V application. It is still OK to hard wire a charger without the neutral wire, but if you put in a receptacle you must run the irrelevant neutral. (Given the current price of #4 or #6 AWG copper, that hurts!)

@Ron Natalie The existing cooktop has a conduit protecting the wires under the cooktop and that goes into the wall. In the garage, I see various conduits going from the direction of the kitchen to the panel. So it looks like everything is in conduit, at least per 1970 standards.

@kaseki The four-burner cooktop requires a 40 amp breaker at 220V. I calculate the actual maximum load around 32 amps, based on the burners supporting 7000 watts of power if all four burners are turned to maximum settings. The actual breaker now installed is 50 amps.

Regarding GFCI, is it required that this be at the breaker instead of inline? If you had an event that could trigger GFCI, it would be a much safer and faster debugging period to just be able to reset the GFCI while you are the appliance, and if it immediately retriggers you know you have a serious problem. Having to potentially go out in the rain at 2 am and reset a GFCI at the panel, only to find out when you get inside that this created a problem, seems like a more dangerous way to organize things.

Of course, an electrician needs to make final decisions about these things. Can I get some education before I call the installer/electrician out to do the install? What is the harm in learning a little about the subject before I formulate my requests?

Regarding GFCI: the application I have heard about most often in the bathroom is someone drops a running appliance into a bathtub. While I realize a cooktop does not have that risk, I am just trying to cover a few more use cases since the appliance is not providing a ground wire. If - for whatever reason - the ground is not done correctly, won't having GFCI in place offer some protection?

Thank you for the comment about the white wire being taped as green if it has been repurposed. I can check for that.

Obviously, the diagram provided by the manufacturer looks wrong, because as you point out it lacks a ground wire. That is why I am posting this thread, and I am trying to understand the issues involved, so I can make the correct request to the installer/electrician, and further so that I can make sure they are addressing all of the issues that get raised in this thread.

@rwiegand What are the wiring differences between NEMA 14-50 120/240V and NEMA 6-50 240V? If I were going to install a plug and receptacle for anything drawing that much power, I would insist on a twist lock plug.

@rwiegand What are the wiring differences between NEMA 14-50 120/240V and NEMA 6-50 240V? If I were going to install a plug and receptacle for anything drawing that much power, I would insist on a twist lock plug.

The only wiring difference is one is two conductors plus ground (three prongs on the plug) and the other adds the neutral (four prongs on the plug). Boxes and conduits need to be sized appropriately for the extra wire. Use the "L" versions for a locking receptacle (eg 6L-50). Both work, the locking is used more typically when connecting something that moves around and might pull the plug out.