The German international's absence will pave way for Brazilian centre-back Gabriel Paulista to start.
Paulista came off the bench to replace Mertesacker in the FA Cup semi-final, and has performed well whenever he has been called upon by Arsene Wenger since signing in January.
This will be his biggest test yet, and his opponent is certain to make life uncomfortable for him.
Chelsea's top scorer Diego Costa is out injured and Loic Remy a doubt, with the next option after Drogba being 17-year-old Dominic Solanke.
Drogba is not the player he once was, with the 37-year-old scoring just six goals this season.
He is nonetheless a figure Arsenal will not want to see. He has scored 15 goals against the Gunners in 15 matches, destroying Arsene Wenger's side over the years with a freakish consistency.
There's little doubt he will be up for this game, and if he starts he will provide the ultimate test for Gabriel to show he is the player Arsenal believe he is capable of being.