Keane's initial month-long deal expired after the Rams' Sky Bet Championship defeat at home to Wigan on New Year's Day but the 20-year-old central defender will now remain with Steve McClaren's side until the end of January.
Keane has started the last three games in place of injured skipper Richard Keogh, whose recovery from a knee problem will take another couple of weeks.
"Manchester United have agreed that Michael can stay until the end of January and can play in the FA Cup. We will then reassess at the end of the month," said head coach McClaren.
Derby are keen to keep England Under-21 international Keane until the end of the season, like they have been able to do with Leicester loanee Zak Whitbread who is fit again after two months out with a calf injury.
Meanwhile, the Rams are in talks with Tottenham over signing attacking midfielder Simon Dawkins, 26, on a permanent basis.
McClaren added: "Hopefully we can do a deal very soon to get him here."
Derby are expected to complete the loan signing of 20-year-old Chelsea striker Patrick Bamford once his loan with MK Dons has expired.
His final game for the League One club is due to be in their FA Cup tie against Wigan on Saturday.