Drogba, 34, suffered the problem in the 1-0 Champions League semi-final first-leg win over Barcelona on Wednesday, having scored the winning goal.
The Ivorian is expected to be fit for the return leg at the Camp Nou on Tuesday, with Fernando Torres set to deputise this weekend.
"Both David Luiz and Drogba will miss the game against Arsenal. Drogba picked up a knee injury against Barcelona and we will need to assess him over the next couple of days," boss Roberto Di Matteo said.
Luiz was expected to miss the match, having been ruled out for at least two weeks with a hamstring injury suffered during the FA Cup semi-final win over Tottenham Hotspur.
Chelsea lie sixth in the Premier League, seven points behind third-placed Arsenal but two shy of the fourth and final Champions League qualifying slot.