Chelsea, who beat Leicester after extra time in the last quarter final just before the draw took place, will face Southampton.
The two games will take place at Wembley on the weekend of the 21st and 22nd of April.
Spurs were drawn as the away side in their tie with United, meaning they will have the unusual experience of using the away dressing room at Wembley. The venue has been their temporary home stadium this season while White Hart Lane is redeveloped.
Tottenham saw off Swansea City to reach the semis for the second successive year, as they aim to win the FA Cup for the first time since 1991.
They will play 2016 winners United, who beat Brighton at Old Trafford in their quarter final. For both sides the FA Cup represents their last realistic chance of silverware after being knocked out the Champions League, and with Manchester City streets ahead in the league.
Last year’s losing finalists Chelsea are also seeking the cup as their final potential honour this season after being knocked out of Europe, and will face a Southampton side currently in the Premier League relegation zone.
The Saints reached the last four after beating Wigan Athletic, conquerors of Manchester City, in new manager Mark Hughes’ first game in charge.
FA Cup Semi-Finals