The 76-year-old – revered as one of the most successful football managers of all time – had emergency surgery on Saturday.
His former club Manchester United said the operation had gone “very well”, but that Sir Alex would need a period of intensive care to aid his recovery.
Sir Alex had appeared fit and well when he presented old rival Arsene Wenger with a memento at Old Trafford last Sunday ahead of the Frenchman’s departure from Arsenal.
Football fans have set allegiances aside to unite in sending their best wishes to one the game’s greats.
United’s arch-rivals Manchester City joined other clubs using the hashtag “football family” to wish Sir Alex well.
City manager Pep Guardiola sent his best wishes for a speedy recovery. “A big hug and our thoughts are with his wife Cathy and the Manchester United family,” he said. “I was glad to have dinner with him two weeks ago and hopefully he can recover as quickly as possible.”
Former United player David Beckham posted a picture on Instagram of himself as a schoolboy with Sir Alex, writing: “Keep fighting, Boss... Sending prayers and love to Cathy and the whole family.”
Cristiano Ronaldo, who was signed by Sir Alex as an 18-year-old in 2003, said: “My thoughts and prayers are with you, my dear friend. Be strong, Boss!”
Former goalkeeper Edwin van der Sar, whose wife Annemarie van Kesteren suffered a brain haemorrhage in 2009 but later recovered, said he was “devastated” to hear the news “knowing all too well about the situation ourselves”.
Rangers FC, for whom Sir Alex played in the 1960s, tweeted: “Everyone at Rangers FC sends their best wishes to Sir Alex Ferguson following emergency surgery.” Aberdeen FC, which Sir Alex managed before Manchester United, also wished him well.
Sir Alex retired in 2013 after 26 years at the helm atOld Trafford. During that time he took the club to the pinnacle of the English and European game, leading United to 13 Premier League titles, two Champions League crowns, five FA Cups and four League Cups.
First Minister Nicola Sturgeon joined Scottish Tory leader Ruth Davidson in tweeting their best wishes.