The England Under-21 international, who spent the latter part of last season on loan at QPR, was diagnosed with a problem when West Ham's players reported back for pre-season testing.
A statement on West Ham's website confirmed the player "had a minor procedure at a central London hospital on Tuesday afternoon."
"The operation was completed without complications and, following a period of rehabilitation, it is expected the England U21 midfielder will return to training in a few weeks when the first-team squad return from New Zealand."
Morrison joined West Ham from Manchester United in January 2012 and has made 17 league appearances for the club.
As well as enjoying a spell on loan at QPR, he spent the 2012-13 season with Birmingham City.