The 20-year-old joined the Craven Cottage outfit late on deadline day, along with United team-mate Ryan Tunnicliffe.
Like Tunnicliffe, Cole has been told by new boss Felix Magath he is surplus to the German's first team plans.
Tunniclife - as Sky Sports revealed earlier this week - has been given permission to discuss loan deals with Ipswich and Wigan.
Cole made his Premier League debut for Fulham after coming on against United in the 2-2 draw at Old Trafford but, since Rene Meulensteen's sacking, has not been involved since.
A statement on the Premier League club's website confirmed the move and added: "The winger will be looking to make an impact at Stadium MK under manager Karl Robinson, with the Dons hoping for a late promotion push in Sky Bet League One."
Robinson said: "I'm really excited by this signing. We've been watching him for a while and he is a high-potential player.
"We had to react quickly to the Samir (Carruthers) injury and he's exactly the type of player I want to bring to the football club - a player of quality, a player of note."