Earlier in the day, Jose Mourinho, the United manager, had said the club were "very positive" Sir Alex would make a full recovery.
In a statement, United said: "Sir Alex no longer needs intensive care and will continue rehabilitation as an inpatient".
'Sir Alex no longer needs intensive care, ' the statement read.
'It was a tough night on Saturday and we were waiting for some positive news.
The update, which was shared by Manchester United's official Twitter page, says that he is now receiving treatment and continuing rehabilitation as an inpatient.
Ferguson, 76, was admitted to Salford Royal Hospital for the procedure on Saturday after a fall at his home near Manchester.More news: Florida mom and her 2 toddlers die after hitting alligator on highway
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After successfully establishing United as the biggest club in England, Ferguson retired from football in 2013, having led the Red Devils to their 20th Premier League title in his final season. "His family request privacy in this matter".
He added: "His household requested for privateness and that's what I'm going to respect".
"He told me he is doing a lot of exercise, and he looked very happy but that kind of accident can happen".
Pochettino said: "I am so pleased, so happy".
The game's governing body Federation Internationale de Football Association sent Ferguson their best wishes as he continues his recovery.
Ferguson spent nearly 27 years as manager of United before retiring in 2013 as the most successful coach in British football history.
He duly did so as United overtook Liverpool as the most successful side in English domestic football. "Hopefully he recovers fully and wishes go to Cathy and the family".