Wawrinka, seeded 25, will play 20th seed Sam Querrey of the United States for a place in the quarter-finals.
In a bizarre match that ebbed and flowed from start to finish, both players needed treatment for thigh strains in the third set, which Wawrinka eventually won to open up a two sets to one lead.
Murray revived his hopes briefly with a break of serve to start the fourth set, but Wawrinka broke back immediately.
Another break to the Swiss player in the sixth game meant there was no way back for an increasingly hobbled-looking Murray, whose US Open hopes, so promising just a week ago, were shattered for another year.
"That's part and parcel of playing that sort of match I guess," Murray said of his injuries which he identified as tightness in his left thigh muscle followed by pins and needles around his right elbow from the start of the third set.
"I hadn't been involved in any long match for some time so whether it was fatigue or not I don't know.
"He played played better than me and that's it. Not any more to it."