Correction Department spokesman Stephen Morello says Michael Enright, of Brewster, N.Y., was taken from the Rikers Island jail to Bellevue Hospital on Thursday night.
Authorities say Enright uttered an Arabic phrase before slashing Sharif's face and neck Tuesday night.
Mayor Michael Bloomberg met Thursday at City Hall with the Bangladeshi driver, Ahmed H. Sharif.
Bloomberg says it's impossible to know the motive but connected the attack to the debate about an Islamic center planned near ground zero.
Police Commissioner Raymond Kelly says authorities do not believe the attack signifies a trend in anti-Muslim crimes.