The teenage winger, who was rewarded for scoring the equaliser at Arsenal last week with his second Premier League start of the season on Saturday, pulled up after 64 minutes at Goodison Park and had to be carried off.
Deulofeu was replaced by Kevin Mirallas, who came off the bench to seal Everton’s win with their fourth goal in injury time.
And manager Roberto Martinez confirmed after the game that Barcelona loanee Deulofeu is likely to be out for the foreseeable future.
"Gerard's injury is a negative. He's a sprinter and he's pulled his hamstring," he told Everton’s official website.
"We don't know how big the tear is but we expect him to be out for a little bit of time.
"We have to be patient to get him ready for an important final third of the season."
The victory extended Everton’s unbeaten Premier League run to nine games and moves the Merseysiders up to fourth in the table.
Everton dominated the early stages of the match and deservedly led at the break courtesy of Leon Osman's opener.
A spirited Fulham side responded well after the interval though, and deservedly drew level through Dimitar Berbatov's penalty before Seamus Coleman, Gareth Barry and Mirallas sealed the hosts' win.
And Martinez was thrilled with the character shown by his side, who he admitted were "mentally fatigued" following two draining away fixtures at Manchester United and Arsenal.
"I was very pleased with the performance in the end," he said.
"First half we controlled the game, we kept Fulham at no shots on target. Second half you have to give great credit to Fulham - they were well organised, pressing us high up, stopping us playing.
"(But our) mindset changed (after the equaliser). We were brave, adventurous and creative in the final third."
