O'Meara won The Open at Royal Birkdale in 1998, but will not compete at Royal Liverpool due to a reported elbow injury.
First reserve Fisher will now contest the third major of the season in his place.
"Field update: Mark O'Meara has withdrawn from The Open Championship and is replaced by England's Ross Fisher," read a statement from the tournament's official Twitter account.
O'Meara is the second American to pull out of the tournament after Steve Stricker opted not to play last week.
Stricker made the decision last year to reduce his schedule to spend more time with his family, and for the second year running decided not to play The Open.
Ryo Ishikawa was called up in his place to compete for the famous claret jug.