Dunning was stretchered off with his neck in a brace after England's dominance up front caused the Wallabies' scrum to collapse.
However, an X-ray at Twickenham showed no major damage and Dunning then underwent an MRI and CT scan in London which also gave him the all-clear.
"I just felt a bit of strain in my neck and the medical staff wanted to make sure we did everything right and be cautious," said Dunning.
"The scans have revealed it's just a joint strain which is good news and I'd like to thank everyone for their concern and support through messages, and also let family and friends know that I'm okay."
With Dunning to receive treatment on the injury and his availability for next Saturday's Test against Ireland uncertain at this stage, the Wallabies will fly in Australia A prop Nic Henderson to join the squad in Dublin.