The Wales international came on as a second-half substitute but was forced off before the final whistle after sustaining the problem.
Ramsey’s substitution came after Per Mertesacker was substituted with a head injury in the first half, and fellow defender Gabriel was brought off with a muscular problem after the break.
Speaking to BT Sport about the injuries after the 4-0 win, Wenger said: “I’m a bit under shock there because we lost our two centre-backs in the game and after we lost Aaron Ramsey.
“Mertesacker is not serious, just a little concussion. I think Gabriel looks right. Ramsey, I’m a bit more concerned because it’s a thigh injury.
“Apart from that we have played well!”
Two goals from Olivier Giroud and two from Theo Walcott handed Arsenal a comfortable win on the night and booked their place in the quarter-finals of the FA Cup, where they will face Watford at Emirates Stadium on Sunday afternoon.
Arsenal took the lead in the 41st minute when Olivier Giroud latched on to David Meyler’s misplaced pass to fire home.
Giroud then fired in Theo Walcott’s cross to make it 2-0 in the 71st minute.
Walcott made it 3-0 with a cool finish shortly after, before adding further gloss to the scoreline in the 88th minute.
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