Martinez and Lindelof started as United’s centre-back pairing at the Emirates Stadium, with the former’s usual partner Raphael Varane absent for “a few weeks” through injury.
However, the Argentine was forced off with a knock of his own 25 minutes from time, while his Swedish colleague also departed 17 minutes later with the game locked at 1-1 after Martin Odegaard’s swift first-half equaliser to cancel out an opening goal from Marcus Rashford.
With Luke Shaw - who filled in at centre-back on a number of occasions last term - also sidelined, United had to see out the match against Arsenal with the oft-maligned Harry Maguire and recent returnee Jonny Evans in central defence, the latter inadvertently deflecting Declan Rice’s crucial 96th-minute Gunners effort beyond Andre Onana at his near post following a corner.
Gabriel Jesus wrapped up victory for the hosts with a superb late solo effort, with United left fuming after a series of important officiating decisions that they feel went against them - not least the ruling out for an apparent marginal offside of Alejandro Garnacho’s slick counter-attack goal that looked to have given Ten Hag’s side a precious late lead.
The sight of both Martinez and Lindelof heading off and fourth and fifth-choice central defenders finishing the game was a real concern for United fans as injuries continue to bite in the early stages of the new campaign.
Asked about Martinez and Lindelof after the game, Ten Hag said: "Victor was ill, so he had to come off.
"And Licha [Martinez] said he had a problem on his foot. But I'm not sure if it's an injury.
"We have to wait, we have to see, we have to make the diagnosis."
United would be at pains to lose Martinez again for any period of time, with the World Cup winner having missed several months earlier this year after surgery to repair a fractured metatarsal. He was also taken off at half-time of the Premier League opener against Wolves at Old Trafford last month.
Ten Hag will be thankful for the timing of the upcoming international break, with United also without the likes of Mason Mount, Tyrell Malacia, Amad Diallo, Kobbie Mainoo and Tom Heaton at the moment as well as Martinez, Varane, Lindelof and Shaw.
There was also no Scott McTominay or Jadon Sancho in the matchday squad to meet Arsenal, with Ten Hag similarly providing an update on that pair after the loss.
“Scott is ill,” he said. "And Jadon, on his performance in training, was not selected. You have to reach a level at Manchester United every day and we can make choices in the front line. So for this game he was not selected."
Sancho later hit back at Ten Hag’s claims about his training efforts in an extraordinary statement posted via his official social media accounts.
He wrote on X (formerly Twitter): “Please don’t believe everything you read! I will not allow people saying things that is (sic) completely untrue, I have conducted myself in training very well this week.
“I believe there are other reasons for this matter that I won’t go into, l’ve been a scapegoat for a long time which isn’t fair! “All I want to do is play football with a smile on my face and contribute to my team.
“I respect all decisions that are made by the coaching staff, I play with fantastic players and (am) grateful to do so which I know every week is a challenge.
“I will continue to fight for this badge no matter what!”
United return to action after the international break at home to high-flying Brighton on September 16, before their Champions League campaign kicks off with a tough trip to Bayern Munich four days later.