He was injured on Saturday during the Wales' second Test against Australia at the Suncorp Stadium in Brisbane.
His fiancée Kate Roberts is staying with him in Australia while he recuperates enough to travel home to Wales.
Chris has already been sitting up in bed and this week is scheduled to take his first steps with the help of a walking frame.
When he is released from hospital, the pair will stay at a private address on the coast near Brisbane until Chris is fit to travel.
WRU Chairman David Pickering said, "On the night Chris was injured I spoke to the Australian Rugby Union President Paul Mclean who made sure one of Australia's finest surgeons was on hand to look after him.
"I now have every confidence that everything possible is being done to help Chris and ensure his treatment is first class and his extended stay in Australia is as comfortable as possible.
"He and Kate will get some time away from Brisbane until he is strong enough to travel which should be pretty soon.
"It was a bad injury but I am certain Chris will bounce back because he is a man of great fortitude and a player of outstanding potential."