The Midlands club said that the former Reading striker suffered severe bruising and a small chip to his right knee following the collision.
Hutton was not penalised for the lunge, which looked late and two-footed.
It leaves Giovanni Trapattoni with limited striking options when the Irish face Estonia in a play-off for the European Championship finals in Poland and Ukraine next summer.
Kevin Doyle is already suspended for the first leg, while Robbie Keane is a major injury concern.
Long's West Brom team-mate Simon Cox started Ireland's last qualifier against Armenia while Stoke City's Jonathan Walters came off the bench in that game. Newcastle's Leon Best may also now come into contention for a place.
The first leg will be played either on November 11 in Tallinn, and the return match in Dublin on November 15.