Williams will return to his club Ospreys to undergo further treatment on the injury and will miss the game against England in Cardiff next week, while the rest of the campaign also looks a no go.
The loss of Williams follows on from the news number eight Taulupe Faletau will also miss the rest of the tournament as he requires more surgery on his broken arm.
A statement on the WRU website read: "Scott Williams has been released from the 2019 Guinness Six Nations squad to continue rehabilitation of his back injury at his Region.
"It is felt that his injury will preclude him from taking a competitive part in the competition. An update will be provided later today regarding players released back to their Regions for action this weekend."