Ferguson is reported to have fallen ill on Saturday (AEST) and admitted to Macclesfield District Hospital before being transferred later to Salford Royal.
The 76-year-old's son Darren - who is Doncaster Rovers manager - missed his team's game with Wigan Athletic on Sunday (AEST) due to "family issues".
And United confirmed on Sunday that Ferguson, their manager for 27 years until 2013, is recovering after a procedure that went "very well".
"Sir Alex Ferguson has undergone surgery today for a brain haemorrhage," a United statement read.
"The procedure has gone very well but he needs a period of intensive care to optimise his recovery. His family request privacy in this matter."
The Scot has been a regular visitor to Old Trafford following his decision to stand down five years ago and was in attendance last Monday to present a gift to long-time adversary Arsene Wenger, who is leaving Arsenal at the end of the season.
Ferguson overcame a slow start at United to preside over a period of unprecedented success, leading the Red Devils to 13 Premier League titles and two UEFA Champions League crowns.
