Saeed, 36, will head to Brisbane from Colombo on August 23 with his test scheduled the next day.
The second one-dayer is scheduled for August 25, and if the tests take longer he will miss the second match as well, a Pakistan Cricket Board (PCB) official told PTI.
Dr Sohail Saleem who heads the PCB medical panel will accompany Saeed to Brisbane.
In the past, Pakistani bowlers reported for suspected bowling actions have undergone tests at the University of Western Australia in Perth and most of them were cleared, including Saeed who was first reported for his bowling action in 2009.
This time the International Cricket Council (ICC) has changed its protocols for testing bowling actions reported by umpires and match referees so the tests are going to be held in Brisbane, the official said.
Saeed, Pakistan's leading bowler in recent years with 178 wickets in 35 Tests and 182 one-day international (ODI) and 85 Twenty20 wickets, was reported after the first Test against Sri Lanka at Galle earlier this month.
The official said umpires and match referee have reported at least 30 to 35 deliveries bowled during the Test in their report.
It is a worrying situation for us because too many deliveries have been reported over the span of the Test and these include his stock off-breaks not just the 'doosra', he said.
The official said the PCB would get the report from the tests in a week's time.
Depending on the results, the ICC can stop him from playing cricket until he works on his action or it can clear him. The world cricket governing body may even ask him to refrain from bowling some of his deliveries.
Apparently the ICC decided to change its protocols for testing suspect actions after too many bowlers were cleared by the biomechanics in Perth.
Pakistan could also be without left arm pacer Junaid Khan in the first ODI on August 23 as he is still recovering from his head injury sustained while hooking a bouncer during the second Test at Colombo.
Junaid has started training with the team but doctors will give him final clearance to play before the match. He might be advised to take more rest, he said.