Halfpenny has not played since suffering concussion against Australia in November and is expected to miss at least the first two games of the competition.
The British and Irish Lions full-back was among the names in Warren Gatland's 39-man squad as he continues his recovery from his latest injury setback.
Young could make his Six Nations debut after he was given the nod along with fellow back-row Josh Turnbull.
Taulupe Faletau misses out after suffering another broken arm on his comeback from the same injury in Bath's win over Wasps last weekend, but Ross Moriarty, Rhys Patchell and Jake Ball were selected.
Jarrod Evans and Jonah Holmes, who made their international bows in November, were also in Gatland's squad.
Wales faces France in Paris in the opening match of the tournament on 2 February (AEDT).
Forwards: Rob Evans, Wyn Jones, Nicky Smith, Elliot Dee, Ryan Elias, Ken Owens, Leon Brown, Tomas Francis, Samson Lee, Dillon Lewis, Jake Ball, Adam Beard, Seb Davies, Cory Hill, Alun Wyn Jones (captain), Ross Moriarty, Josh Navidi, Justin Tipuric, Josh Turnbull, Aaron Wainwright, Thomas Young.
Backs: Aled Davies, Gareth Davies, Tomos Williams, Gareth Anscombe, Dan Biggar, Jarrod Evans, Rhys Patchell, Jonathan Davies, Hadleigh Parkes, Owen Watkin, Scott Williams, Josh Adams, Hallam Amos, Steffan Evans, Leigh Halfpenny, Jonah Holmes, George North, Liam Williams.