The woman, Florence Cioffi, was pronounced dead at NYU Downtown Hospital.
Anderson left the scene in his black Mercedes Benz SUV, but later returned.
He was charged with vehicle manslaughter, leaving the scene of an accident and criminally negligent homicide.
Anderson, who lives in Glen Head on the North Shore of Nassau County, declined a breathalizer test. Detectives obtained a court order for a blood test and he was taken to NYU Downtown Hospital.
Charges of driving while intoxicated could be added, pending the results of the test.
Anderson told police that he was a computer programmer, but they soon learned he worked at Enterprise Engineering, a privately held software and information technology consulting company on Broadway.
He has been the chairman and CEO since its creation in 1995, according to officials.
Enterprise Engineering's Web site claims its clients include Merrill Lynch, JP Morgan Chase, Morgan Stanley, Fidelity Investments, Wells Fargo, Putnam Investments, Lehman Brothers, UBS, Union Bank of California, MetLife and Visa.