Harry Maguire's late own goal came after he replaced Raphael Varane at half-time
United looked to be coasting to a quarter-final first-leg victory at Old Trafford thanks to Marcel Sabitzer's first-half double.
However, after Antony had hit the crossbar, Sevilla came back into the contest and profited from a terrible ending to the game for Erik ten Hag's men.
First Tyrell Malacia diverted the ball past David de Gea after former Manchester City man Jesus Navas had pulled a low cross back from the goalline.
Then, two minutes into injury time, Youssef En-Nesyri's off-target header struck Harry Maguire to leave De Gea helpless as it flew into the net.
The scoreline is bad enough as it leaves United facing a battle to secure the semi-final spot they seemed to have virtually sealed.
However, the loss of Martinez is a major concern, particularly as Raphael Varane had to be replaced at half-time.
Martinez had to be carried from the field by his Argentina team-mates Gonzalo Montiel and Marcos Acuna and then left for the dressing room on a stretcher in obvious pain after catching his foot in the turf with no opponent near him.
--- Courtesy of BBC Sport