The American shot-stopper sustained the injury in the fifth-round replay against Oldham Athletic, meaning Jan Mucha will continue to deputise against the Latics at Goodison Park
The injury, which the American shot-stopper sustained in the fifth-round replay against Oldham Athletic 10 days ago, is unlikely to sideline Howard until the end of the season, but back-up Jan Mucha will continue to deputise in his absence, having made his Premier League debut against Reading last weekend.
Moyes said: “Tim is out against Wigan. He has broken two bones in his back. We don't think he will be out for the season.
"I read that [Newcastle defender Fabricio] Coloccini could be out for seven weeks but we are not sure how long Tim will be out for because, obviously with a goalkeeper, he has to dive around and hit the ground.
"I have let him go away for a few days. It might be that, if everything goes well, he misses next week's game as well [against Manchester City] and then because of the international break he might be close after the rest because that would be four weeks.
"He has two fractures, but they are not bones that are supporting anything. It is off the spine. They are not weight-bearing.
"It just needs a bit of healing time. It is not like a pure fracture where you need to wait to look at it. It is a question of whether he can cope with the pain. The bones will heal themselves but it's not good."
The Scot also confirmed that Phil Jagielka will be unavailable for the tie as the Toffees look to book their place in the semi-finals for the second season in a row, with a gashed foot keeping the defender sidelined.
"We think it won’t be too long before he is back," Moyes added. "Hopefully we get him back quite quickly," he added.