The Spanish under-21 international, on loan from Barcelona for the season, suffered the injury in Saturday’s 4-1 win over Fulham, which moved Everton within four points of league leaders Arsenal.
Deulofeu was making just his second start of the campaign against Fulham after being rewarded for a brilliant equalising goal off the bench in the 1-1 draw at Arsenal the previous week, his second strike of the campaign.
“Scans have now shown the extent of the soft tissue injury in his right hamstring, which is likely to keep him out for a few weeks,” Everton said in a short statement on Monday.
The Merseysiders, who are fifth in the league after 16 matches, travel to Swansea City on Sunday before hosting Sunderland (December 26) and Southampton (December 29).
They then travel to Stoke City on January 1 before their FA Cup third round tie against Championship (second division) leaders Queens Park Rangers on Jan 4.