The 52-year-old had been in an upstate New York hospital for more than a week, his lawyer Josh Grier said.
The Emmy-winning songwriter, possibly most well-known for his band's smash hit "Stacey's Mom," had been on a ventilator for the bug.
Schlesinger won two Emmys and was nominated for Grammys, Tonys and Oscars. He was nominated a total of 10 times for Emmy awards, five of them for his work as the executive music producer for "Crazy Ex-Girlfriend."
The other five nominations include contributions to "Sesame Street," a Stephen Colbert Christmas special and the Tony Awards.
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