The 33-year-old striker suffered the problem during the Blues' 6-0 home win against Arsenal in the Premier League on Saturday.
Eto'o, who had opened the scoring at Stamford Bridge, was replaced by Fernando Torres in the 10th minute.
"Hopefully it's not so big," Mourinho told Chelsea's official website. "Hopefully it's not a one-month injury, it's 10 to 15 days."
Chelsea are currently at the top of the league table with 69 points from 31 matches.