The England international is currently recovering from an ankle problem which has sidelined him since the defeat at Tottenham Hotspur on 3rd March.
Wilshere will again be sorely missed in Saturday's game against Reading and the trip to West Bromwich Albion on 6th April as Arsenal nervously chase the UEFA Champions League.
But, having also been rocked by the loss of Abou Diaby for up to nine months with a knee ligament injury, Wenger does not want to take any gambles.
"Jack will start his first run outside on Monday and six days that will be too short (for the trip to West Brom)," said Wenger, who also has Theo Walcott on his injured list.
"Jack has been out for four weeks on Monday. He works very hard inside in the gym but it is not the same.
"If we lose Jack, then we quickly are short in central midfield."
Wenger added: "Wilshere's injury is not better or worse. It was an inflammation of his (ankle) bone and we had such history with him we are a bit more cautious than we would be with you or with me.
"We will rest him when it is needed. He has regular scans and as soon as we have an alert we will respect it no matter what is at stake."