The Championship side held Sunderland to a goalless draw at the Stadium of Light last month, meaning a replay will decide who goes on to face Bradford City in round five.
Johnson, who scored a hat-trick on his last visit to Craven Cottage, has ruled himself of the encounter, but says he will not be sidelined for long.
"Unfortunately I won't be there," he told the Sunderland Echo. "I'm getting an operation on my thumb.
"I'll be missing this one. I just have to get it done, it's not a serious thing.
"But I need the wound to heal. It's the risk of infection that's keeping me out.
"It's the best time to do it with the games coming up, though.
"I love playing at Craven Cottage, so I'm disappointed to miss it, but I have to have it done, so hopefully the lads can get through without me.”
