Lukaku was stretchered off after colliding with team-mate Gareth Barry as Steven Gerrard headed Liverpool in front in the 21st minute of Tuesday's derby at Anfield.
Martinez expressed concern about the extent of the injury after the game, saying "it does not look good", but he was able to offer a more positive prognosis on Wednesday.
"There is no ligament damage and the injury is not as bad as we first thought," he told the Everton website.
"It will be a case of weeks rather than months."
Lukaku, 20, has scored nine goals in 20 games for Everton since signing on loan from Chelsea last year.
Romelu Lukaku out for weeks rather than months: Everton
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