That would then leave the Gloucester centre with just one more game - against France at the same venue seven days later - before Ashton announces his 30-man World Cup squad on August 14.
Tindall, who has won more than 50 caps, is recovering from a broken leg suffered during Gloucester's Premiership clash against Newcastle in April when he collided with England colleague Toby Flood.
A fully fit Tindall would contest England's outside centre position alongside Mathew Tait, but time is not on his side.
Ashton said: "We probably need to make some sort of call over the next couple of weeks.
"It is ongoing rehab with Mike, but of all the players who are currently rehabbing he is well behind the others.
"It is highly unlikely the way things are at the moment that he will be fit for the Wales game."
Tindall was one of England's form players during the RBS 6 Nations Championship campaign last season, scoring a superb try in the Twickenham victory over France, and he is a key figure in Ashton's World Cup plans.
Having already lost Tindall's 2003 colleagues Ben Cohen and Julian White from England's Webb Ellis Trophy defence in September and October for family reasons, he will not want to see the Gloucester player ruled out.
But while Tindall continues on a difficult road back to full fitness, Ashton has delivered a vibrant medical report regarding uncapped Bristol number eight Dan Ward-Smith.
Ward-Smith has not played since suffering a serious knee injury in January, but he has made rapid strides in recent weeks, so much so that he has now resumed full training and looks certain to be in strong contention for a World Cup place.
Ashton added: "I am delighted with him.
"Not that long ago it looked less than 50/50 for him, but he is back in and doing full training with full contact."
Ward-Smith spent some time in America with renowned knee specialist Bill Knowles, and Ashton believes that has undoubtedly speeded up the recovery process.
"The work he did in the USA has pushed him along really, really well," Ashton concluded.