The NI Ambulance Service said staff responded to an emergency call just before 9am, close to Belfast City Hall, and that two people had been injured.
The millionaire businessman confirmed he was one of the two people taken to hospital, but said that although he was hurt, he did not suffer any serious injuries.
"I’m shocked and badly shaken but out of hospital and trying to recover. I don’t want to speak much about it now,” he told the News Letter on Tuesday evening.
Mr Lavery said the incident happened quite suddenly, but declined to elaborate as an investigation is underway.
The condition of the second person involved is not known.
The Short Strand man won a £10.2m National Lottery jackpot in May 1996 while working as a bus driver in the city.
He featured in a BBC documentary last month, speaking about his venture to return whiskey distilling to Belfast after 90 years.
Mr Lavery was earning less than £200 a week when he became an overnight multi-millionaire.
In the BBC’s Our Lives: The Lottery Millionaire and the Spirit of Belfast, Mr Lavery retells how that incredible life-changing moment enabled him to give up his day job after 10 years with with Citybus Ltd and embark on a series of ambitious projects.
The film follows the progress of Mr Lavery’s ambitious plans for a floating distillery in the Titanic Pumphouse, and also the launch of a new River Lagan tour boat.
Looking back to the time of his lottery win, the film documents how he coped with the turmoil of going from a low wage earner week to becoming one of Northern Ireland's richest people in an instant.
He also describes how his newfound wealth almost killed him.
Speaking in the documentary, Mr Lavery says: “It’s been a labour of love and near put my head away, but it’s worth it.”