"Welbeck is very sharp but he's not out of it completely. We have to be cautious," Wenger told reporters on Monday.
"Physically, he's ready but we have to manage the times we use him. To come out of what he's gone through you need to be mentally strong."
Wenger said Welbeck was unlikely to feature in Tuesday's Premier League clash against 14th-placed Watford.
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"That's not a gift of God, you have to go through all kinds of suffering to get to that... I don't know how we will use him after three days, I think he's a bit short for that," he added.
Wenger made 10 changes for the FA Cup fourth-round victory at Southampton and the Frenchman is confident his squad has enough depth to compete on all fronts.
"I believe number-wise and quality-wise, we have what is required to do well," he said.
"It's down to us to perform and to produce with the quality of our focus, the quality of our ambition and desire to produce the performance in every single game.
"I believe we have what is required to do well, now it's down to us."
Despite having no bids on the table for Carl Jenkinson and Mathieu Debuchy, Wenger is still open to offers for the right backs and he denied reports suggesting the north London club are trying to lure striker Karim Benzema from Real Madrid.
Arsenal are second in the league table with 47 points, eight behind Chelsea after 22 games.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Ed Osmond)
