As permanent skipper Alun Wyn Jones is injured, Biggar will lead his country for the first time, with lock Adam Beard vice-captain.
Centre Jonathan Davies and flanker Ellis Jenkins, who have captained Wales in the past, are also in the squad.
Ospreys hooker Dewi Lake and flanker Jac Morgan and Cardiff forward James Ratti are the uncapped players.
As well as usual skipper Jones, Wales' lengthy injury list includes fellow Lions Ken Owens, Taulupe Faletau, Dan Lydiate, Josh Navidi, Justin Tipuric, George North and Leigh Halfpenny.
Dragons flanker Ross Moriarty has been named in the squad with Wales hoping he will have recovered for the start of the tournament after suffering a shoulder injury against New Zealand in October 2021.
Wales begin the defence of their Six Nations title against Ireland in Dublin on Saturday, 5 February.