The South Atlantic News Agency is reporting that the 61-year-old was airlifted to King Edward Memorial Hospital in Stanley.
His injuries are not life threatening.
There were apparently six people in the car, including former international team-mate Ricky Villa, which overturned at around 9pm local time.
"Ardiles and Villa had to be rescued by a military helicopter... four of the injured were discharged and three remain under observation," a news website in their homeland said.
A spokesperson from the Falkland Islands Government later confirmed the details of the incident, with no further updates yet available from the hospital on Ardiles.
"I can confirm that there was a road traffic accident involving seven passengers last night in the Islands. Thankfully, due to the fast action of our rescue services and the British forces, they were successfully evacuated to hospital in Stanley, where their injuries were assessed," she said.
"Three members of the party remained in hospital overnight for observations and further treatment, and the remaining four were released from hospital following treatment for minor injuries."
Ardiles and Villa were part of the 1978 World Cup winning Argentina side on home soil and both won the 1981 FA Cup with Spurs.
Ardiles went on to manage Newcastle United between 1991 and 1992.
He replaced Jim Smith at St James' but when things turned sour he too was replaced, this time by Kevin Keegan.