The Wales full-back was hurt during the dramatic closing seconds at the Millennium Stadium on Saturday. He had earlier kicked four penalties to put Wales within sight of victory.
Halfpenny, 23, was taken to Cardiff's University Hospital Wales, where he underwent scans after complaining of neck pain.
"He was immediately admitted to hospital to exclude any serious neck injury, a process which thankfully has now been concluded," the Welsh Rugby Union said, in a statement on Sunday morning.
Cardiff Blues player Halfpenny added: "I want to say thank you to all of the medical teams who have looked after me following my injury.
"The paramedics, WRU and Millennium Stadium medical teams were outstanding. All of the staff at University Hospital Wales were also amazing.
"Everyone has been so supportive, and the care that I have had has been incredibly professional and second to none.
"I would also like to thank all of those who have been sending me messages of support following the injury."
The WRU added that Halfpenny would now undertake a period of treatment and rehabilitation to ensure a swift return to play.
Halfpenny, a major contender to tour Australia with the British and Irish Lions next summer, was Wales' outstanding performer during an autumn series that produced losses to Argentina, Samoa, New Zealand and Australia.
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