Lynagh, who had missed both tests against South Africa last month with concussion, was replaced during the second half due to a tight hamstring before being asked to take a head injury assessment test by the match doctor.
"Tom Lynagh has undertaken his HIA2 post-game and HIA3 today," the Wallabies said in a statement on Monday.
"At no point did he ever have concussion symptoms despite the result of his HIA1 being off his baseline, which could have been due to other factors at the time.
"Tom is therefore cleared of concussion and is continuing to be monitored for the right hamstring that forced him from the field on Saturday."
Lynagh made his first three starts for the Wallabies in the British & Irish Lions series in July and August but missed the matches in South Africa after a high shot by Dan Sheehan in the third Lions test left the flyhalf with concussion.
The Australians will face Argentina again on Saturday in Sydney with Joe Schmidt's side sitting in second place in the Rugby Championship standings after three games, one point behind New Zealand.
