The 61-year-old was detained in hospital overnight after having stitches inserted in a head wound. His injuries were described as 'not serious'.
Argentina and Spurs team-mate Ricky Villa, also 61, was one of seven people in the car which is believed to have overturned after swerving off a road, but he was not kept in hospital.
Ardiles' son Pablo confirmed his father was not seriously hurt, saying: "My understanding is that he is fine. He has had 20-odd stitches in his head and has been hospitalised overnight.
"Ricky Villa and my brother were out there too but they are okay and back in the hotel."
A spokesperson from the Falkland Islands Government said: "There was a road traffic accident involving seven passengers last night.
"Thankfully, they were successfully evacuated to hospital in Stanley, where their injuries were assessed.
"Three members of the party remained in hospital overnight for observations
and further treatment, and the remaining four were released following treatment for minor injuries."
Ardiles and Villa were part of Argentina's 1978 World Cup-winning team before the pair headed 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.