Anscombe made his full international debut for Wales against Ireland in August last year as a second-half replacement. He was called into the Welsh squad during last year's Rugby World Cup after Gatland's side suffered a rash of injuries.
Fullback Leigh Halfpenny and centre Scott Williams also miss out on the Six Nations squad with injury, but utility back Liam Williams and lock Jake Ball are both included despite being side-lined.
Despite being unlikely to make the 2019 World Cup, 35-year-old prop Gethin Jenkins keeps his place, as does No 10 Rhys Priestland, who moved to Bath in the summer.
'We have selected a squad that rewards players form as well as picking a lot of experience and that continuity is important to us,' said Gatland.
'We have picked a larger squad than normal, we have a few injuries at the moment, those players aren't too far away from getting back on the field so we are happy with the mix.
'It is always exciting when the Six Nations comes around and we are looking forward to meeting up next Monday.'
WALES SQUAD FOR THE 2016 SIX NATIONS (37 players):
Forwards:
Props: Rob Evans (Scarlets), Paul James (Ospreys), Gethin Jenkins (Cardiff Blues), Tomas Francis (Exeter Chiefs), Aaron Jarvis (Ospreys), Samson Lee (Scarlets). Hookers: Scott Baldwin (Ospreys), Kristian Dacey (Cardiff Blues), Ken Owens (Scarlets). Second row: Jake Ball (Scarlets), Luke Charteris (Racing 92), Bradley Davies (Wasps), Dominic Day (Bath Rugby), Alun Wyn Jones (Ospreys). Back row: Josh Turnbull (Cardiff Blues), Taulupe Faletau (Newport Gwent Dragons), James King (Ospreys), Dan Lydiate (Ospreys), Ross Moriarty (Gloucester Rugby), Justin Tipuric (Ospreys), Sam Warburton (Cardiff Blues).
Backs:
Halves: Aled Davies (Scarlets), Gareth Davies (Scarlets), Lloyd Williams (Cardiff Blues). Fly-halves: Dan Biggar (Ospreys), Rhys Priestland (Bath Rugby). Centres: Cory Allen (Cardiff Blues), Jonathan Davies (Clermont Auvergne), Tyler Morgan (Newport Gwent Dragons), Jamie Roberts (Harlequins). Wings: Hallam Amos (Newport Gwent Dragons), Alex Cuthbert (Cardiff Blues), Tom James (Cardiff Blues), George North (Northampton Saints). Fullbacks: Gareth Anscombe (Cardiff Blues), Matthew Morgan (Bristol Rugby), Liam Williams (Scarlets).
- Daily Mail