His former club Manchester United said the procedure had gone “very well but he needs a period of intensive care to optimise his recovery”.
“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,” a club statement said.
Bryan Robson, who played until 1994 and remains Manchester United’s longest serving captain, told Sky Sports News: “It did come as a big surprise and a shock, but from what I’ve heard the operation went well and hopefully The Boss will have a full recovery.”
Sir Alex’s son Darren Ferguson, who is manager of Doncaster Rovers, missed his team’s match against Wigan on Saturday due to “family reasons”.
A statement from the League One club said: “Darren asks for privacy, and will provide an update through the club during the week.”
Sir Alex appeared on the pitch at Old Trafford a week ago to present outgoing Arsenal manager Arsene Wenger – his long-time rival – with a trophy recognising his career.
The 76-year-old retired from managing United in 2013 after 26 years in charge and remains the most successful manager in British football history.
At United, he won 13 Premier League titles, two Champions League crowns, five FA Cups and four League Cups.
He famously won the treble in 1999 after securing the Premier League, FA Cup and Champions League in one season.
Messages of support quickly flooded on to social media following news that Sir Alex had suffered a brain haemorrhage, or bleeding on the brain.
Manchester United captain Michael Carrick said he was “absolutely devastated”, while goalkeeper David De Gea said he was praying for his former manager.
Former United star David Beckham urged Sir Alex to “keep fighting” as he shared a photograph of the pair together when he signed for the club as a schoolboy.
A host of football clubs also voiced support for Sir Alex including United’s rivals Manchester City and Aberdeen, where he managed for eight years.
Liverpool FC hailed Sir Alex as a “great rival but also a great friend” and it hoped for his “full recovery”.
He began his playing career with Scottish club Queen’s Park before having spells with St Johnstone, Dunfermline Athletic, Rangers, Falkirk and Ayr United.
He retired as a player in 1974 and began his managerial career at East Stirlingshire before going to St Mirren, where he won the Scottish first division title in 1977.
Sir Alex moved on to Aberdeen where he won three Scottish titles, four Scottish FA Cups, one League Cup and the European Cup Winners’ Cup in 1983.
He managed Scotland in the 1986 World Cup in Mexico following the death of Jock Stein and became Manchester United manager later that year.
He was knighted in 1999 after his treble success.
Sir Alex announced his retirement in 2013, winning the Premier League title in his final season.
He later said he took the decision to spend more time with his wife Cathy after her twin sister Bridget died.