Ardiles was on the Falklands to film a documentary with former Spurs team-mate Ricky Villa when the accident happened, leaving him needing 20 stitches to the head.
Villa suffered minor injuries in the accident and has since been discharged from hospital.
Ardiles remains in the King Edward VII Memorial Hospital in the island town of Stanley, but confirmed he is not badly hurt via a statement released by the Falklands Island government.
"Thank you to everyone in the Islands who has helped, without exception," the statement read.
"From the moment of the accident, the attention and care we have received from the police, the RAF helicopter team, the doctors and nurses here have been world class.
"Thank you to everyone for your concern, I am fine and doing well."
Villa confirmed some details about the accident, telling Todo Noticias: "The road that we were going through wasn't good, the car jumped twice, we are worried because it was a difficult moment that we had to go through.
"Osvaldo, and the guy in charge of the sound of the documentary that we are filming and a cameraman are the only three that had to remain at the hospital.
"The thing was that Osvaldo, who was driving, tried not to roll over a lamb that suddenly appeared on the road, so he lost control of the the car."
Meanwhile, a Tottenham statement read: "All at the club wish Ossie Ardiles and Ricky Villa speedy recoveries after they were involved in a car accident in the Falklands on Monday evening."
Ardiles and Villa, both 61, were among seven people in the car which is believed to have overturned after swerving off a road.
The pair were part of Argentina's 1978 World Cup-winning team before both heading to London to join Tottenham later that summer.
While at White Hart Lane, they were part of the Spurs team which won the FA Cup in 1981, with Villa scoring the winner against Manchester City in the replay at Wembley.
Ardiles went on to manage Tottenham, Newcastle and West Bromwich Albion.