The 19-year-old Australian has played a big part in United's rise to the top of the table, scoring four times in his 13 starts.
That loan, due to expire on January 1, has now been extended for the rest of the campaign.
"It's good for everyone concerned," manager Chris Wilder told the club's official website.
"Ryan is a talented player and has done well for us. He is enjoying his time here and Fulham can see him gaining experience and playing well."
Williams added: "I have really enjoyed it here and had no hesitation at all in staying. The club is in a great position right now and I am looking forward to playing my part in the second half of the season."