Sinclair is alleged to have been involved in a domestic disturbance that saw the police called.
But the BBC pundit had left the scene by the time officers arrived, only to be later found after seemingly hitting a pedestrian with his car around a 10 minute drive away near his home in Lytham St Annes on the Lancashire coast.
A police spokesperson said, "Police were contacted at 8.45pm yesterday (Sunday, November 12) to a report of a disturbance at a house on Victory Boulevard in Lytham.
"Officers attended the property and found a man had already left the property in his car, a Tesla X60d. A short time later officers found the vehicle which had been involved in a collision with a woman pedestrian on Clifton Drive. She received minor injuries.
"The driver, a 44 year old man, was arrested on suspicion of drink-driving, common assault and criminal damage. He is currently in custody."
Prior to his arrest, Sinclair had made a comment on social media regarding what he described as 'racist' police officers. His use of 'again' also suggests there have been other disturbances and/or incidents in recent weeks or months that have led to police being called.
"Racist old bill all over the Sinclair residence again tonight. Thank god as a black man I've not fallen asleep again," the 1997 Match of the Day 'Goal of the Season' winner tweeted.
Sinclair retired from football in 2008 after a short spell with Cardiff. He played 12 times for England, including at the 2002 World Cup, and had also turned out for Blackpool and QPR during his career.
He is now a qualified UEFA coach and had previously been assistant manager at non-league Lancaster City during the 2014/15 season.