Callender was co-captain for last year’s two-Test series against Australia – leading the side to a historic first win Down Under – and the World Cup in England.
The 25-year-old overcame an ankle injury to feature in the tournament but then needed surgery after Wales’ early exit.
She returned for Harlequins at the end of January and it is believed to be a fresh injury and not a relapse.
Williams, who made her Test debut against Ireland in 2023, shared the captaincy duties and has been chosen as the leader for the Six Nations.
Lynn said: “Kate Williams has the respect of the whole squad, and her leadership skills means she will be Wales captain for this Six Nations campaign.”
Wales lost all five games of last year’s championship, condemning them to a second Wooden Spoon on the bounce.