Smith said that he wants to be 100 per cent fit.
"It's certainly an area of concern, concussion, and I want to be 100 per cent fit. I've got to be able to train a couple of days out and then face fast bowling to make sure my reaction time is in place. There are a few tests I'll have to tick off and time will tell," he said.
Smith was ruled out of the remainder of the second Ashes Test a day after being hit on the neck by England pacer Jofra Archer. After being hit by the ball, Smith left the field but made a comeback after clearing the concussion test.
However, Smith said he felt 'a little bit groggy' on Sunday morning.
"I started to feel a little bit of a headache coming on last night probably as the adrenaline got out of my system. I was able to get a good sleep in which is somewhat rare for me, but woke up feeling a little bit groggy and with a headache again," he said.
"I had some tests done and upon some further assessments (it was) deemed to be a mild concussion, unfortunately, and have been ruled out for the rest of this Test match," Smith added.
Marnus Labuschagne has been approved as Smith's replacement.
The third Ashes Test between Australia and England will start from August 22.