"The procedure has gone very well but he needs a period of intensive care to optimise his recovery," a statement from the club said. "His family request privacy in this matter."
United captain Michael Carrick tweeted: "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, the manager of Doncaster Rovers, was reported to have missed his team's match on Saturday for family reasons.