The Uruguay international made his first appearance of the 2021-22 season as a substitute in the Premier League clash with Wolverhampton Wanderers before the international break.
Cavani has since missed the matches with Newcastle United and Young Boys, with Solskjaer revealing that the experienced striker had picked up a knock in training.
The 34-year-old will also be absent against West Ham United in the Premier League on Sunday but could potentially be available for the EFL Cup fixture with the Hammers next week.
"Edinson hopefully will start training with us after the weekend, maybe Monday, so maybe involved on Wednesday. He had a fantastic season last season, the impact he made when he got his fitness, he struggles with niggly injuries early on," Solskjaer told reporters.
"We feel that to get the best out of him this season we need to get him 100% fit and not rush him. We've got a strong squad that will cope with having to let players heal and not risk any further injuries.
"I see Edinson having a massive impact, he's that type of personality and player. He can't wait to play and he's working really hard to get back on the pitch."
Cavani has scored 17 times and registered six assists in 40 appearances for Man United. body check tags ::