Terry Sandford, 41, of Bexleyheath, Kent, is believed to be in custody at Heathrow airport, just hours after he met police to hand over a briefcase which Pinsent lost in the car park.
Sources said Sandford was being questioned by detectives.
Scotland Yard would say only that a 41-year-old man was in custody helping with their inquiries in connection with the theft.
Pinsent was reunited with the priceless medal - won 10 days ago in Sydney - at lunchtime after a frantic morning.
Few tears
"I didn't cry when I won the medal but I shed more than a few tears when I realised I'd lost it," he said.
Pinsent was being interviewed by BBC News 24 when he was told that the medal had been handed in by a taxi driver.
Pinsent's agent Athole Still told Reuters: "An unidentified man driving away from (Heathrow's) terminal three handed the briefcase containing the medal to a taxi driver who was arriving at the airport."
The taxi driver contacted Still after finding an envelope with his address on in the case.
"He (the taxi driver) said he had a fare to Leatherhead, so I told him not to worry, to take the medal back to Heathrow after Leatherhead," said Still.
Girlfriend
Pinsent had been at Heathrow to meet his girlfriend, Demetra Koutsoukos, who was flying back from Australia via Toronto.
Before learning that the medal had been found, Pinsent had told Five Live that he was devastated at the loss.
"I've had my little cry and I managed not to cry when I was awarded it but now I've lost it I've gone a little bit pear-shaped.
"It means so much to me and to the country as well," said Pinsent.
The rower made an impassioned appeal to the thief to leave the brown leather briefcase somewhere safe so his medal could be returned.
Replacement
Philip Pope, a spokesman for the British Olympic Association, said it would have been possible to get a replacement medal if Pinsent's had not been returned.
He said: "There is a historical precedence for it and in the last few years we got a new one made for a pre-war winner who had lost his.
"Happily we won't have to do it this time, " he said.