Wenger lamented what looks like a third hamstring injury of the season for Ramsey as the Welsh midfielder went off just nine minutes after coming on as a second half substitute.
He was also critical of heavy Leicester tackling that saw Chile winger Sanchez taken off with a knock following a clash with Matthew Upson at the Emirates Stadium on Tuesday.
“I don’t know (the extent of the injury) but it is not good news,” Wenger said of Ramsey. “He’s had a recurrence now of a few injuries.
“Sanchez had a knock with his knee and I don’t think he was himself. From the moment he got his knock, he was never comfortable. I don’t know how long he’ll be out. It was a heavy tackle, yes.”
First-half goals from Laurent Koscielny and Theo Walcott gave Arsenal what Wenger described as an “important” response to Saturday’s derby defeat to Tottenham, and kept them right in the middle of a tight race for the top four.
Arsenal overcame an impressive Leicester start with Koscielny side-footing in from a corner on 27 minutes, before Walcott volleyed home after 41 following Mesut Ozil’s powerful parried effort.
Despite that lead, they lost energy in the second half, and Wenger put it down to the effects of last week’s north London derby.
“The Spurs defeat was a bit in the head and, especially second half, in the legs. I have seen Tottenham has lost 3-2 to Liverpool as well in the final minutes. It was a very intense game,” he said.
Wenger also backed Leicester, who previously had to deny reports that they sacked manager Nigel Pearson, to stay in the Premier League despite their position at rock bottom.
“When you see the way they (Leicester) play football, it is a surprise they are bottom of the league and want to get rid of their manager.
“If they keep quiet, don’t panic, they will survive, because they are one of the better sides we have played.”