The .mtl (and texture files) should be output into the same folder as the .obj, and I'm unaware of a setting to prevent it. Do command About Photoshop and tell us which version of Ps is reported. Also tell us which OS version you are running.
WIndows 7 Pro
Files are nowher to be found...weired. Have a second station at work and that has no issue.
Does the station at work have an earlier version? Maybe a recent Photoshop update has screwed up something on your home computer. I'm still using 13.0.1 on a Mac. Hopefully, someone with 13.1.2 x64 on Windows can check this for you.
I just ran a simple OBJ export with Win7 x64 (SP1), Ps 13.1.2 x64 and the .mtl is present. What format for textures did you choose? How many texture files does your layer have?
To cut a long story short, I cleared cache, temp files and rebooted - all worked OK.
New obj files now have materials. I deleted the "bad" versions.
Thanks for your help.