A United statement said the procedure “had gone very well” but Ferguson “needs a period of intensive care to optimise his recovery”.
The Scot, 76, retired as United manager in May 2013 after winning 38 trophies during 26 years in charge. He was at Old Trafford last Sunday when he presented Arsenal boss Arsene Wenger with a commemorative trophy.
Ferguson’s family have requested privacy as he recovers in Salford Royal Hospital.
“We will keep Sir Alex and his loved ones in our thoughts during this time, and we are united in our wish to see him make a comfortable, speedy recovery,” United later said in a tweet.
The most successful manager in the history of the British game, Ferguson’s trophy haul at Old Trafford included 13 Premier League titles, two Champions League crowns, five FA Cups and four League Cups.
Ferguson famously won the Treble of Premier League, FA Cup and Champions League in 1999, the year in which he was knighted.