Hines had started last Sunday's defeat to France at Murrayfield and had again been named in the side for the trip to the Welsh capital.
"Nathan suffered a calf strain and aggravated an old ankle injury during the match at the weekend," said Scotland and Lions doctor James Robson.
"Whilst the injury has settled considerably, it is not at a level adequate for exposure to the rigours of Test-match rugby and therefore Nathan is withdrawn from selection."
The news will be a big blow to Scotland head coach Andy Robinson, with Hines just one of four Scots to have represented Britain and Ireland's elite last summer.
Hines has been replaced in the Scotland XV by Edinburgh's Jim Hamilton after the former Leicester lock bypassed Richie Gray for a place in the side.
Glasgow youngster Gray had been named on the bench for both the French and Welsh games but Robinson has instead opted to draft Hamilton straight into the starting line up for his 24th cap.
"I welcome Jim back into the squad following his own recovery from injury," said Robinson.
"We're going with Jim as he's our like-for-like with Nathan and will help us to get a platform should we look to get our mauling game going. Jim is also an experienced player."