The Brazilian-born Spain international, who has scored 19 league goals in his first season in English football, injured a hamstring soon after coming on as a halftime substitute in last weekend's home game against Stoke City.
Mourinho said it would be "normal" to miss the next four games, which would mean Costa returning against Crystal Palace at the start of May.
With a seven-point lead, Chelsea need 15 more from eight games to regain the title they last won under Carlo Ancelotti in 2010.
Mourinho told a news conference that he would not leave out midfielders Cesc Fabregas or Nemanja Matic from Sunday's west London derby away to QPR, although both are only one yellow card away from suspension.
"The game is a three-point game," he said. "It doesn’t make any sense to think about some matches and not about others. We have to play with our maximum power.
"Nobody is expecting an easy match. Last weekend we played against a team that is very stable in the middle of the table and they were fantastic in their approach, their commitment, trying to win the match or not lose it."
Chelsea have been top of the table since the third game of the season, which their manager said shows "consistency, stability, dominance".
He would not be drawn, however, on transfer speculation involving Japanese striker Yoshinori Muto of FC Tokyo, whom Chelsea are reported to have made a bid for.
(Reporting By Steve Tongue; editing by Toby Davis)
Share
