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The U's are the lowest-ranked team left in the competition, while League One side Rochdale, who knocked out Nottingham Forest, welcome Stoke City.
Holders Arsenal visit Brighton, and Chelsea will play Bradford City, who defeated Millwall in a reply.
Manchester City host Middlesbrough and Bournemouth travel to Aston Villa. Ties will be played 23-26 January.
"It's a game to look forward to," said Cambridge United head coach Richard Money. "It is reward for everyone's hard work at the club.
"Everyone's suffered during nine years out of the Football League but a lot of people have worked hard and now we've got a draw like this."
Liverpool face a home game against Championship outfit Bolton Wanderers, while West Ham will travel to Bristol City.
Sheffield United, who beat Queens Park Rangers in the third round, visit fellow League One side Preston North End.
Manchester United, 2-0 winners at Yeovil on Sunday, have won the FA Cup a joint-record 11 times.
Cambridge, who are 14th in League Two, beat Luton 2-1 at the Abbey Stadium in the third round.
Manchester United and Cambridge last met in the League Cup in 1991, when the Reds won the two-legged tie 4-1 on aggregate.
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League Two side Cambridge United have been drawn at home to Manchester United in the fourth round of the FA Cup.