Zamora has been ruled out for four months after sustaining the break just above his right ankle in Saturday's 2-1 Premier League victory over Wolves.
The 29-year-old England striker, who has undergone surgery, will face a longer lay-off if further damage to the ankle is discovered.
Fulham overcame his first-half departure to complete a last-gasp comeback victory sealed by Dembele's first league goals.
The £5million summer signing from AZ Alkmaar has impressed since his arrival at Craven Cottage and now has a crucial role to play.
With Andy Johnson still several weeks from a first-team return following his battle with a knee injury and Zamora out for four months, Dembele has become a key player.
"We hope Moussa can get the goals - there's a big onus on him now that Bobby's gone," said Cottagers boss Hughes.
"But it's a big ask, you can't just hang a hat on Moussa. He'll get good support from the guys around him and that will help him become the success we think he will be.
"The beauty of Moussa is that he can play in a number of positions.
"That's the attraction from my point of view because I like players who have that flexibility."
Dembele fired the equaliser against Wolves with a well directed, if tame, shot and then blasted an injury-time free-kick through the wall for the winner.
Hughes was aware of the 23-year-old when he was Manchester City manager and reacted immediately when he learnt of his availability.
"Moussa is always very positive, everything he does has a positive slant on it. That's the key to the way he plays," he said.
"He can drive the game and is an intelligent footballer.
"I kept track of him because I've always been impressed with him.
"When it was flagged up that he was in the last year of his contract and likely to be sold, we moved quickly."