The duo picked up problems in the Gunners' shock 2-1 defeat to Watford at the Emirates.
Chelsea's 1-1 draw at Liverpool has kept their faint Premier League title hopes alive, despite their result last night.
But Arsene Wenger now has another midfielder sidelined after Ramsey was substituted with a muscle injury after just 20 minutes.
Alex Oxlade-Chamberlain managed to finish Arsenal's game against Watford despite picking up a knock
I don’t know how long he will be out for, but it’s a calf strain
On the Wales international, the Arsenal boss said: "It’s a calf strain. I don’t know how long he will be out for, but it’s a calf strain."
Ramsey was criticised by supporters for his part played in Watford's opening two goals as they took an early foothold in the clash.
Oxlade-Chamberlain replaced Ramsey from the bench following his impressive display in the middle at Southampton in Saturday's 5-0 FA Cup triumph.
But he also appeared to be struggling as Arsenal were battling back against Watford, with the England ace hobbling around.
Arsenal's Aaron Ramsey is set for a spell on the sidelines after suffering a calf strain
Alexis Sanchez looks absolutely distraught after Arsenal's defeat to Watford
Tue, January 31, 2017
Alexis Sanchez looked absolutely distraught after Arsenal's defeat to Watford
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Arsenal lost 2-1 to Watford on Tuesday
Arsene Wenger's Arsenal now need to earn a positive result at Chelsea to stay in the title race
Wenger had made all three of his changes when Oxlade-Chamberlain was limping, although he managed to see out the match.
On his situation, the manager added: "He got a kick on his knee, yes.
"No I don't think [he'll be a doubt for the Chelsea game]. I think he should be alright."