The procedure on the former Manchester United manager has gone very well - according to the club.
However, they say he needs a period of intensive care to optimise his recovery.
United added that the 76-year-old's family have requested privacy in the matter.
United midfielder Michael Carrick said on Twitter: "Absolutely devastated to hear about Sir Alex being unwell in hospital. All my thoughts and prayers are with him and his family. Be strong Boss."
Ferguson's son Darren, manager of League One side Doncaster, did not attend his side's final home game of the season against Wigan due to his father's illness.
Former United striker Mark Hughes, speaking after his Southampton's side's draw with Everton, said: "I only just got a little whisper earlier on. I was hoping it wasn't true. I wish him all the best."
Messages of goodwill for Ferguson poured in from United players past and present.
Jesse Lingard said on Twitter: "Thoughts and prayers sir alex."
Luke Shaw tweeted: "Sending my love and best wishes to sir Alex."
Peter Schmeichel tweeted: "Please Be strong Win this one."
Nicola Sturgeon, the First Minister of Scotland, said on Twitter: "My thoughts are with Alex Ferguson and his family - wishing him a full and speedy recovery."
Ruth Davidson, the Scottish Conservative leader, tweeted: "So many people will be wishing Alex Ferguson well and sending their thoughts to his family tonight."
Everton manager Sam Allardyce said: "It is tragic. I am going to find out how he is as soon as I possibly can. Obviously I knew it was extremely serious when I knew his son Darren didn't attend his own game at Doncaster today.
"I hope he is in good hands and I hope the operation is a major success because as a personal friend...I hope he has a full recovery."
Ashley Young, whom Ferguson brought to Old Trafford in 2011, said on Twitter: "Gutted to hear the news tonight about Sir Alex. Don't really know what else to say other than thoughts and prayers with you and your family, Boss."
Mike Phelan, who played under Ferguson for United and later served as his assistant manager, said on Twitter: "#SirAlex You've won more than most and if anyone can you can boss."