Robson was in Bangkok when he had the operation on March 3 and United have said specialists are optimistic about the chances of a full recovery.
"Bryan Robson underwent an operation to remove a tumour from his throat on March 3, 2011 in a hospital in Bangkok," a club statement read.
"The laboratory report revealed a cancerous tumour, which will need further treatment. The oncologist is confident that the condition is treatable."
The former Manchester United skipper is currently combining his work as a United ambassador with coaching the Thailand national team.