"He had the operation on Monday and it went well, although we won't know the exact details until he gets back," United boss Sir Alex Ferguson told MUTV.
"He has to have a further operation on his left knee in a few weeks.
"The reason for us sending him out to America was because Richard is a first-class specialist who deals with these sorts of injuries, and Owen's own preference was to be in Colorado.
"Unfortunately he is out for the season, but we hope this will now be put to bed and we'll get him back as a fit player for the start of next season."
Hargreaves has made just 25 starts for United's first team since joining the club from Bayern Munich in August 2007.