"injury sustained" is correct and usable in written English.
You could use it to refer to an injury that has happened, for example: "The victim suffered an injury sustained in a car accident".
It was an injury sustained from hazing.
Coyer died of complications from an injury sustained in Afghanistan.
He missed all of last season with a left shoulder injury sustained during the preseason.
His development was hampered by a hamstring injury sustained during the off-season camps.
The reason for this is a knee injury sustained following a period of medical rest.
Two days later, he died from a head injury sustained in the attack.
Drobny was short-sighted, because of an injury sustained playing hockey, and wore dark glasses.
He missed six games last season with a broken foot, an injury sustained during training camp.
But Bure's newest knee injury, sustained Friday night, might mark the beginning of another plunge.
This was only the Chilean's third start on his comeback from the injury sustained at Norwich.
Owens has been limited by a groin injury sustained Dec. 8 against Dallas.
