The 54-year-old, now Thailand's national team coach, had an operation to remove a tumour in Bangkok on March 3, United said in a statement on Wednesday.
"The oncologist is confident that the condition is treatable," the club added.
"At this moment, Bryan is fine to continue with his role as Thailand coach and his role as Ambassador of Manchester United."
Robson, who was capped 90 times for England, replaced compatriot Peter Reid as Thailand boss in September 2009 to take up his first international coaching position.
"He's out of hospital, he's doing very well and he's keen to get straight back to work," one of his personal assistants told Reuters while accompanying Robson to an AFC Cup game between Chonburi and Hong Kong's South China, 80 km east of Bangkok.
Robson has so far struggled to find a successful formula as Thailand coach and his reign has been disappointing.
The national team last year failed to reach the Asian Cup for the first time in 23 years and were bundled out of the Southeast Asian Games and the Southeast Asian championship - competitions they have long dominated - in the opening rounds.
Robson has said he is fully committed to the job, but needs urgent reforms in the Thai football structure and better cooperation with the domestic league to bring success to the national side.
United said Robson made 461 appearances for the club scoring 99 goals between 1981-1994.
Nicknamed 'Captain Marvel, the combative midfielder helped the Old Trafford side win two Premier League titles, three FA Cups and the European Cup Winners' Cup.
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