Alexander has been named as a run-on reserve while Australia's most-capped Test prop Al Baxter is promoted into the starting line-up in the tighthead position.
Wallabies coach Robbie Deans revealed Dunning initially suffered the injury during the victory over Ireland in Melbourne almost a fortnight ago and that it had been given two days to settle down in the hope the prop would still be available.
"It re-bled after training on Tuesday causing him some discomfort," said Deans.
"We made the call at that stage to place Ben Alexander on stand-by and brought him back down from Brisbane on Wednesday before making the call this morning to withdraw Matt from the Test.
"It wasn't coming right as soon as we'd have liked so we made the decision before training this morning that it was in the best interests of all of the parties involved that we make the call now and move on."
Deans, however, has no doubt Alexander will slot seamlessly into the squad.
"He's ready to go and did his job well for Australia A last Sunday," Deans said. "It is a great opportunity for him."
Alexander admitted his inclusion had come as a surprise. "I didn't actually know I'd be involved until Robbie told the whole team at training this morning," he said.
"Up until then, I was under the impression that I was just there as cover but it was a massive feeling to learn that I'd be part of it. I can't wait."
The 23-year-old ACT Brumbies prop has packed down on both sides of the scrum during training with the Wallabies.