The shot-stopper was not involved in the 3-0 away win against Tottenham in the Premier League on Sunday.
Mendy, who has firmly established himself as the club's no.1 since signing from Rennes last summer, is not expected to miss too many more games.
Tuchel said: "We tried throughout the week and yesterday in training it was so-so. It comes from the last-minute kick against Zenit in the Champions League.
"It is very painful and did not feel 100% comfortable going for a full stretch or to land on it. He didn't feel comfortable at fight at set-pieces or corners.
"So we decided to go with 100% and that was Kepa and have Edou with us to be supportive and have good energy. I'm happy Kepa a crucial role today and kept a clean sheet. This is what he deserves and I am happy that he could."
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