Reports yesterday revealed that the 26-year-old had withdrawn from the squad before even taking part in a single full training session, and would return to Manchester immediately.
Martinez suffered the blow in the 3-0 win over Leicester City on Sunday, but played through the pain and completed 90 minutes without much fuss.
Before the injury could be assessed by the Man United medics, Martinez quickly jetted off for Paraguay, where Argentina are playing in the early evening on Thursday.
There was major travel disruption in Martinez getting to Asuncion, and that is believed to have aggravated the issue even further, with the player now on his way back to Carrington to be inspected more thoroughly.
Martinez to miss Amorim debut?
Speaking to the press ahead of their clash with Paraguay, Argentina boss Lionel Scaloni revealed that "the pain increased" regarding Martinez's issue when he joined up with the squad.
The medical staff have also confirmed that the problem is a "significant hip injury", and was caused following a collision in the win over the Foxes at the weekend.
Once Martinez returns to Carrington, it is unlikely he will be able to join up with new manager Ruben Amorim's first few training sessions, as it is believed the issue is making him unable to function normally at present.
That makes the defender a major doubt for the clash with Ipswich Town when club football returns in just over a week, and leaves Amorim short on options at the back.
Defensive crisis already facing Amorim?
Amorim will want to get off to the best start possible, and while they will be big favourites to beat newly-promoted Ipswich, the new manager may be forced to play with a makeshift defence.
Martinez's injury means he joins Harry Maguire on the treatment table, with the England international unlikely to feature until December.
The versatility of Martinez has also been useful to the Red Devils this season, with him also able to fill in at left-back, but with Luke Shaw still out and Tyrell Malacia only in the very early stages of his comeback, that could be another problem position.
Having started 10 of Man United's 11 Premier League games so far, Martinez has been one of the more dependable players despite their difficult start, with their defensive record ranking as one of the best in the division so far.