My guess is that as long as it isn't directly underneath some huge point load (like a valley rafter or the jack studs of a large-headed opening above) the answer is "probably".
If the framing was laid out neatly, there is another stud bay or rafter bay above the joist bay you're using. Make the hole as neatly as possible, try not to destroy the band. If you would feel better, add a vertical 2x4 leg on the flat to each side of the hole. This will support the bottom plate above you, and hopefully prevent the band from crushing under load.
Casey

You could also add another piece of wood same size, with same hole cut out, and screw securely to original - then you're doubling up that section - of course it has to be a reasonable length, at least as long as the distance between the nearest two joists the original rests on, or what it's supporting above.

Just checking, this is an ordinary piece of wood not an 'engineered' joist? You can't usually cut those.

Hey guys! please answer my question, i have the same situation but my rim joist completele cut, as i wanted 10” duct for my huge new range hood. the guy who installed it said that as joists on a left and right sides of the hole are nailed to the rim joist, as well as subfloor holds all joists together with the rim joist so nothing will happen. What do you think? Is it that inportant to have rim joist solid or reinforced? Maybe I have to reinforce it with some metal brackets? Thanks!!

Never let mechanical trades cut wood. It needs to be reframed.