Erie County sheriff's deputies said the front driver's side tire was missing when Barnaby, 38, of Clarence, N.Y., was pulled over about 3:15 a.m. The Buffalo News reported.
Barnaby failed field sobriety tests and refused to take a Breathalyzer test, the newspaper said. He was booked for DUI and later released to the custody of his lawyer.
Hours after news of the arrest broke, ESPN issued a statement saying Barnaby had been dismissed as a hockey analyst, USA Today reported.
"We spoke with Matthew and informed him we terminated his ESPN contract, effective immediately," ESPN spokesman Josh Krulewitz said.
The retired player was arrested on domestic violence charges involving his ex-wife last spring. He pleaded guilty to misdemeanor charges.
Barnaby played seven seasons for the Buffalo Sabres before going on to the Pittsburgh Penguins,Tampa Bay Lightning, New York Rangers, Colorado Avalanche, Chicago Blackhawks and Dallas Stars in an NHL career that stretched from 1992 to 2007.