Martial became the first French player in Monterrey's history after he joined the side last summer in a deal that lasts until next year.
The 30-year-old, who made 317 United appearances and scored 90 goals during a nine-year stint at Old Trafford, has struggled since leaving the club.
He has found himself at AEK Athens in 2024 after a failed loan at Sevilla and has failed to impress in Liga MX so far.
Now, will be out of action for four to six weeks after leaving the stadium in an ambulance this week due to a serious injury as the club released a statement.
"Club de Futbol Monterrey reports that player Anthony Martial suffered a dislocated right shoulder during the match day 6 game against Leon at BBVA Stadium.
“Anthony's recovery prognosis is subject to change."
The Frenchman has scored only one goal in 19 matches for Monterrey and with his latest injury, fans will be disappointed as he continues to fail away from the Red Devils.
Monterrey reportedly paid around £3.6M to bring Martial to the Estadio BBVA in what has been a failed move so far.
Sunday's 1-0 win over Leon saw them Monterrey move up to sixth in the Clausura in what has been a poor season under manager Domènec Torrent.