Police say Williams reeked of alcohol and refused to take a Breathalyzer test.
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Along with cuts on his face, Williams also suffered a small fracture of a bone in his neck.
The arraignment took place via a video link between the courthouse in Lower Manhattan and Bellevue Hospital, where Williams has been since the crash. He didn't enter a plea Thursday.
Prosecutors say Williams told a police officer he was "sorry for causing trouble" about an hour after the incident.
His bail was set at $5,000 cash. He will have to wear an alcohol monitoring bracelet if released. The charges against him carry a maximum term of one year behind bars.
Williams retired from the New Jersey Nets in 2000. He is awaiting retrial on a New Jersey manslaughter charge stemming from a 2002 shooting at his house that left his limousine driver dead.
The jury deadlocked on the reckless manslaughter count, acquitted Williams of aggravated manslaughter and convicted him of covering up the shooting. He was never sentenced for the cover-up counts, pending the outcome of the retrial, and has remained free on bail. It wasn't immediately clear how the drunken driving case would affect his bail status there.