Flansburgh was being driven home from the alternative rock band's first gig on a pandemic-delayed tour.
Meanwhile, the driver of the car police said instigated the smash in Manhattan's East Harlem neighbourhood was awaiting arraignment on Friday after being arrested on DUI and other charges.
Writing from a hospital bed, Flansburgh told fans he was taking a car service home from Wednesday's show at Manhattan's Bowery Ballroom when the car was T-boned, flipped onto its side, and started smelling of motor oil and smoke.
According to police, the driver who was arrested ran a red light, jumped a kerb and ploughed into the gate of a housing complex, hitting two other cars along the way.
Everyone in all three cars were taken to hospital, police said.
Flansburgh, 62, wrote he had suffered seven broken ribs, some of them fractured in multiple places.
Formed in the early 1980s by Flansburgh and John Linnell, They Might Be Giants rose to fame with clever, catchy songs and a not-afraid-to-be-geeky persona.
Known for tunes including Birdhouse in Your Soul and Boss of Me, the theme tune to TV hit Malcolm in the Middle, the duo went platinum with the 1990 album Flood.
Flansburgh wrote that even as he sat in a CT scanner shortly after the accident, he was thinking about how to get back on the road.
"Someday we will rock again - and for me, that day couldn't come soon enough," he wrote.
But for now, "I will be watching reruns of Sex in the City until I am strong enough to reach the remote".
"Wish me luck," he said. "I'm going to need it."
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