The 22-year-old confirmed that he will return to training Thursday after a week away, but it's understood he'll face a club fine from manager Jose Mourinho, according to the Guardian's Jamie Jackson and Steve Brenner.
It's believed Martial could be fined as much as £180,000 for his failure to return to training earlier under the supervision of Mourinho's staff.
Ahead of United's match against Milan last week, Martial left the team to travel to Paris, France, for the birth of his son, Swan Anthony. A week later, after a victory over Real Madrid, Mourinho claimed he had no idea when Martial would return, according to Luke Edwards of The Telegraph.
On Wednesday, Martial took to Twitter to thank fans for their support and appeared to hit back at Mourinho by stating that his "family will always come first."
"Thanks for all your posts," Martial wrote. "My little Swan is fine but for the mother it is harder. Thanks to God she is better now. Sorry but my family will always come first, back tomorrow in Manchester."
It's the latest chapter in a troubled relationship between Mourinho and Martial, who's expected to maneuver his way out of Manchester following a season in which he struggled for playing time.