The England international has a mild inflammation on his ankle and will miss Wednesday’s trip to Bayern Munich as well as Saturday’s visit to Swansea City as a precaution.
Wilshere will also sit out England’s back-to-back World Cup qualifiers in San Marino and Montenegro but could be back to face Reading at Emirates Stadium on March 30.
“Hopefully for the Premier League he will only miss one game because after [the Swansea game] is an international break and hopefully we can slowly prepare him,” said Wenger.
“At the moment I noticed in the last two games he had to dig deep because he played 30 games [including his preparation matches]. For us it is not welcome, but maybe for him it is not too bad that he has a little breather.
“It is more about prevention. We trust people who are specialists in this area and they told us we have to stop him for a short period.
“Of course, you ideally want him there with us [in Bayern],” added Wenger. “He was out for 17 months and we had to deal with it, so we must be able to do it for two or three weeks.”