I assume your talking about natural gas?
Only because I have been looking myself, the shallow-est fireplace I have found was 13". They significantly go up from there! And it also depends on how your going to vent it, cause those need space too! I don't think there is one single minimum number cause fireplaces come in all different shapes and sizes.

Your best bet is to go to a dealer directly knowing what your space specifications are. They will be able to direct to you a brand and style better then anyone and save you some leg work.

<b>mmonika</b> is correct. Manufactured fireplaces vary a great deal, and it is important to speak with someone who does this all the time to help you with your requirements. You can find a fireplace expert at the National Fireplace Institute website: http://nficertified.org.

The shallowest gas fireplace that comes to mind that still looks looks a little like a fireplace is the Heat & Glo <b>Soho</b>: http://www.heatnglo.com/Products/Soho-Gas-Fireplace.aspx?page=Specifications
It's only 11 1/2" deep.

The <b>Solaris</b> is shallower at 5 1/2" deep, but it doesn't look much like a fireplace to me. But it is cool, no doubt: http://www.heatnglo.com/Products/Solaris-Gas-Fireplace.aspx?page=Specifications

the photo below is the <b>Soho</b>

The above is all good advice.

We needed the shallowest fireplace available to install in several units of our client's new apartment building. We found this 9-1/8" deep, direct vented, glass-front fireplace a great value at just over $2000/each.
http://www.woodlanddirect.com/Fireplace-Accessories/Direct-Vent-Fireplaces/Napoleon-WHD31-Plazmafire-Direct-Vent-Fireplace

We should note that while there is also a ventless version available in states that do allow ventless gas fireplaces on the premise that their efficiency burns nearly all of the gas (all except CA presently), units must be kept in absolute tip top condition to maintain this performance and it is strongly advisable to install combination fire/carbon monoxide alarms (now required in Los Angeles) if you decide to go this route.

The shallowest gas insert

we've found is a Heatilator Ion series (Ion-H7, -S7, and -V7) with a depth of 7 7/8".