Wilshere, 20, is struggling with a stress fracture in his foot and time is running out for him to force his way into the squad for this summer's finals.
Wenger said: "I will not take any risks with him. He is making slow progress so we still have to monitor the situation a little bit at the moment.
"The next three weeks will be decisive.
"We are now in mid-April, the Euros start in the middle of June.
"Jack has not played the whole season and for anyone who knows what is required at the top level, in terms of intensity, time is getting short now."