The England striker has not featured for the north London side since late April due to the minor problem but is not set to make his return at Old Trafford against his former club.
There was some good news for Arsenal, however, with midfielder Aaron Ramsey on course to be available for selection after returning to training with the north London side on Friday.
However, Alex Oxlade-Chamberlain, Mikel Arteta and Mathieu Debuchy all remain sidelined ahead of the Gunners’ trip to Old Trafford.
“We have a similar squad available to has been available recently,” Wenger told a news conference on Friday morning.
“Welbeck is short a fraction but is not far away from returning. We would have loved to have him available but we will have to do without him.
“Ramsey I think will be alright.”
Arsenal head to Old Trafford looking to return to winning ways after their surprise 1-0 defeat by Swansea City at Emirates Stadium on Monday night.
The north London side are currently third in the table heading into their final three Premier League games of the season.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news