Zamora suffered the damage to his right leg during a hard challenge from Wolves skipper Karl Henry in Saturday's Premier League clash at Craven Cottage and received oxygen before being carried off on a stretcher and taken to hospital.
Fulham manager Mark Hughes revealed that he could be out for longer if surgery reveals further damage.
"If the injury is as we think it is, it's likely to be four months," he said.
"If the surgeon goes in tomorrow and finds other damage rather than just the break, which is four centimetres above his ankle, it will be even longer than that.
"The four months looks like a minimum."
Hughes remonstrated with referee Phil Dowd on the pitch after the half-time whistle had blown but later conceded Henry's tackle was not malicious.
"It's a shame but I don't really lay the blame on the player (Henry). It's one of those," said Hughes.
"There's always a danger if you get tackled from the side or from behind that players' legs can get trapped.
"I don't think there was any intent to hurt Bobby. You don't expect the circumstances of the injury to be the result of a challenge like that, but it can happen.
"At the time I was a little bit disappointed that the referee didn't view it as a foul, but there you go."
Zamora won his first England cap last month and only missed the recent Euro 2012 qualifiers because of a thigh problem, leading Hughes to lament the timing of the injury.
"Bobby had got to a point where he was playing at a high level and producing week-in, week-out," said Hughes.
"Bobby would be honest enough to admit he hasn't been able to maintain that level of performance over long periods during his career.
"But he's reached that point so to be taken out of top level football for four months is a real disappointment for him and us.
"I've spoken to him already and he seems to be in good spirits."