The Manchester United star had been chasing back into his own half when he pulled up, clutching his calf.
Martial, 23, signalled to the bench and after a brief assessment he was replaced.
The French striker had equalised for the home side, taking advantage of slopping defending from a free-kick to slot home from close range.
It was his eighth goal of the season for United – scored on his 23rd birthday.
Jose Mourinho's team had found themselves trailing after a Marcos Rojo error was pounced upon by substitute Alexandre Lacazette.
But United hit back 74 seconds later, Saed Kolasinac making a massive mistake of his own for Jesse Lingard to take advantage.
It is not yet clear how serious Martial's injury is, with Mourinho so far not giving any update on the state of the forward.
In a sloppy 2-2 draw at Old Trafford, all four goals came from defensive errors.
Shkodran Mustafi opened the scoring after David De Gea spilled the ball and Ander Herrera failed to clear.
Martial then equalised before the home side gifted Arsenal another goal – this time, Marcos Rojo getting caught in possession and Alexandre Lacazette scoring before Lingard's equaliser.
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