The 23-year-old cyclist was pedaling west on West 21st Street when he passed through the red light at Ninth Avenue and was hit by a cab driver in a Toyota heading southbound at about 11:30 a.m., police said.
Police didn't say how investigators knew the cyclist ran the red light.
The cyclist, who wasn't wearing a helmet, suffered a severe head injury and was listed in critical condition at Bellevue Hospital, police said.
The cabbie, a 22-year-old man, stayed at the scene and wasn't immediately arrested or charged, police said.
Police don't suspect any criminality, but said the investigation is ongoing.