The highly-regarded 19-year-old arrives with Callum Kennedy still not ready to return from an ankle injury and could make his Dons debut in Saturday's League Two clash at Fleetwood.
Richards is yet to feature for Fulham's first team but has impressed for their Under-21 Development side.
Dons boss Neal Ardley told the club's official website: "With Fulham being local to us we've watched Tom play several times for their Under-21s.
"He's been playing at left-back this season but he has unbelievable energy up and down the left side. I went and watched the player last week in a game against Leicester and he stood out in that match.
"Tom is not tall but he is quick, has great stamina and a really good left foot. He's played left-back and left midfield both equally as well. Tom will therefore give us a lot of balance on that side as regards the wing-back role or if we wanted to change the shape slightly."
Ardley continued: "Callum will not be training for a little while yet as he's still trying to get over his ankle injury. The wing-back role is also very demanding and you need three or four weeks of intense training to get in peak shape for it.
"Jim Fenlon has been playing there and doing a job on the left even though he is naturally right-sided. With seven games coming up in March we felt that this was an area that we needed to strengthen."