The forward made his first start of the season scoring twice in the 5-0 win over Southampton in the FA Cup on Saturday following a cartilage injury.
But Arsenal boss Wenger is conscious not to overload him.
He said: “Danny’s very sharp but we’re still not out of it completely. We still have to be cautious with him.
“Where I agree is that physically he is ready to play. We still have to manage the times we use him and the times we rest him for a while.
“We will do that in the next month and then after, hopefully he will be completely fit.
Danny Welbeck scored twice as Arsenal thumped Southampton
Danny Welbeck celebrates first Arsenal goals after injury
Sat, January 28, 2017
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“To come out of what he has come through, you need to be mentally strong. To play like he played on Saturday, you need to work hard physically.
“That’s not a gift of God. You have to go through all kind of suffering to come back to that level of fitness.
“Of course he has done enough to keep his place but at the moment we have to be cautious with him. I’m not sure how we’ll use him every three days. I think he’s a bit short for that. But the quality of the performance was there.
“We have scored many goals since the start of the season and Danny was not there. To add him to the squad as well gives us huge offensive potential.
“Now I have to use the strikers well, in the right moment and without destroying the balance of the team. Offensively, we have many players who can produce and score.”
Danny Welbeck is still feeling his way back from injury
Carl Jenkinson could still have an Arsenal future
Meanwhile admits the chances of Carl Jenkinson leaving for Crystal Palace are diminishing but has refused to shut the door on the defender going.
He said: “There’s no news about him at all.
“We are still open because we have many players in his position, but at the moment it doesn’t look like something will happen.
“We respect any professional decision. Carl Jenkinson is a great player who has a great attitude. There is no problem on that front. After that, he must find happiness with his conditions and where he goes and feel comfortable.”