Manager Roberto Martinez has confirmed the Belgium international did not sustain a serious injury in the 4-0 defeat in Tuesday night's Merseyside derby at Anfield.
Lukaku was carried off on a stretcher after colliding with team-mate Gareth Barry as they tried to prevent Steven Gerrard scoring the first goal in the 21st minute.
"There is no ligament damage and the injury is not as bad as we first thought," Martinez told evertonfc.com.
"It will be a case of weeks rather than months."
Lukaku has scored nine goals in 20 appearances since joining on loan from Chelsea in the summer.
He joins the likes of Bryan Oviedo (broken leg), Arouna Kone and Darron Gibson (both knee) and Seamus Coleman and Sylvain Distin (both hamstring) on the injury list.
Everton will contact Liverpool after a number of concerns were highlighted by visiting fans about access problems to Anfield.
"We are aware of a significant number of complaints regarding queue management from supporters waiting to enter Anfield at last night's derby match," said director of communications Alan Myers.
"The club will make contact with Liverpool Football Club to raise these matters."