Mustafi limped off in the first half of Arsenal's 3-1 defeat to Manchester United on 2 December with what Arsene Wenger later revealed to be a thigh problem. The Gunners boss had hoped for the Germany international to be back for Sunday's trip to Southampton, but again the defender was a notable omission from the squad as the North London side rescued a late point on the south coast.
Per Mertesacker stepped in to replace his compatriot in that contest, and the veteran centre-half could be called upon again with Mustafi still unavailable for the trip to East London.
Ramsey, meanwhile, suffered a hamstring injury in the draw against Southampton, with reports suggesting the Wales international will be sidelined for three weeks.
Offering an injury update ahead of the West Ham game, Wenger told a press conference: "Mustafi will not be back, we lost Ramsey against Southampton, and he will not be available tomorrow. Everyone else, apart from long-term injuries, everyone is available, we will have tests this morning to see how they have recovered."
Wenger hopes to have Mustafi available once again for the visit of Newcastle United on Saturday, however. "[Mustafi will be] a little bit longer, he is out in training running but not playing yet and the medical staff decide he is not ready. Will he be ready on Saturday? Maybe, yes."
Wenger also sought to reassure fans over the extent of Ramsey's latest problem, insisting he only expects the midfielder to be ruled out for a "short period".
Wenger added he will have to check the fitness levels of some of his players before deciding to make changes for Wednesday night.
"I have not made the decision [on my team] completely, I will look at how some players have recovered [from the Southampton game]."
Santi Cazorla is Arsenal's only other absentee as he continues to recover from a long-term Achilles problem.