Developers of 20 Fenchurch Street, better known as the "Walkie-Talkie" because of its distinctive shape, are investigating reports of the damaging glare, and a number of nearby car parking spaces have been suspended, say reports.
Businessman Martin Lindsay said he was distraught when he returned to find his luxury Jaguar XJ saloon with warped panels along one side.
The wing mirror and badge had also melted from the heat of the reflected sunlight, he claimed.
"They’re going to have to think of something. I’m gutted. How can they let this continue?" he told City AM .
Another driver has also come forward to complain of damage to his Vauxhall Vivaro van.
Eddie Cannon, a heating and air conditioning engineer, said: "The van looks a total mess - every bit of plastic on the left hand side and everything on the dashboard has melted, including a bottle of Lucozade that looks like it has been baked."
The 37-storey skyscraper is still under construction.
In a joint statement, developers Land Securities (LSE: LAND.L - news) and Canary Wharf, told the newspaper: "As a precautionary measure, the City of London has agreed to suspend three parking bays in the area which may be affected."