The Cardiff Blues player has not yet been ruled out of the World Cup or Wales' warm-up matches against Ireland on 29 August and Italy on 5 September.
Wales head coach Warren Gatland selects his final 31-man squad on 31 August.
A Welsh Rugby Union spokesman said: "Gareth did pick up an ankle injury in training last week and he is continuing to be assessed at the moment."
New Zealand-born Anscombe made his Wales debut as a second-half replacement during the World Cup warm-up defeat to Ireland.
That display was enough to see the 24-year-old survive Gatland's first reduction of his squad, from 46 to 38 players.
One of Anscombe's rivals for the fly-half berths, James Hook, was among those to be discarded.
He is now vying with Dan Biggar, Rhys Priestland and Matthew Morgan for a place in Gatland's final selection.
Anscombe, whose mother is Welsh, joined Cardiff Blues from Super 15 side Waikato Chiefs in July 2014.
Wales fly-half Gareth Anscombe is a doubt for the World Cup after injuring his ankle in training.