The 19-year-old is available for the Dons' trip to Stevenage in League One on Saturday.
"He's quick, he's a good size and I like the fact he's grounded in the Swansea way. I believe his dad used to play too so there's football in his blood," manager Karl Robinson told the club's official website.
"I had a good chat with him and he's a well-mannered young man. He can play anywhere across the top three but he ultimately wants to be a number nine. He's something different and he can handle the ball well too.
"It's his first loan spell away and he needs to adjust from Under-21s football to men's football. But, he wants to get better and we're excited at the prospect of working with him."
MK Dons are currently in seventh place in the League One table, six points adrift of the playoff places.