Wainwright, who has 50 caps, was their best performer in the 25-16 first Test defeat in Sydney last weekend but tore a hamstring in the dying stages.
Winger Josh Hathaway suffered an elbow injury in the same clash and will also miss the Melbourne Test on Saturday.
But in better news for Gatland, veteran fullback Liam Williams and prop Gareth Thomas were declared fit after suffering knocks in Sydney.
Wales are desperate for a win having last tasted a Test victory against minnows Georgia in the pool stages of the 2023 Rugby World Cup. They have not won a Test in Australia since 1969.
Another defeat would edge them closer to the record run of 10 losses in 2002 and 2003 when New Zealander Steve Hansen held the coaching reins.
"This week, we've been going through our processes, building on what worked well and sharpening the areas that need improvement," said Gatland.
"We expect Australia to go up another level this weekend and we know we need to as well."
With Wainwright out, Taine Plumtree will move to No. 8 with James Botham, grandson of England cricket great Ian Botham, coming into the starting line-up at blindside flanker.
Tommy Reffell completes the back row at openside flanker.
Cameron Winnett was named at fullback after being overlooked for Sydney, with Williams moving to the wing alongside Rio Dyer.
Team (15-1)
Cameron Winnett; Liam Williams, Owen Watkin, Mason Grady, Rio Dyer; Ben Thomas, Ellis Bevan; Taine Plumtree, Tommy Reffell, James Botham; Dafydd Jenkins, Christ Tshiunza; Archie Griffin, Dewi Lake (capt), Gareth Thomas
Replacements: Evan Lloyd, Kemsley Mathias, Harri O'Connor, Cory Hill, Mackenzie Martin, Kieran Hardy, Sam Costelow, Nick Tompkins
