The 25-year-old Brazilian missed Saturday's defeat by Tottenham Hotspur after picking up the injury during a training session on Friday.
"He has an injury on his thigh, and he is going to be out for a few weeks," Alonso told reporters. "Let's see how many; we don't want to predict on that, but he's not ready for the next games."
Pedro has made a bright start to the season, scoring five goals and providing three assists in seven appearances across all competitions.
Alonso acknowledged the loss of the Brazil international but said Chelsea had the depth to cope with his absence.
Chelsea will face Liverpool on Wednesday in the League Cup last 16 and host Manchester United in the league on Saturday.