The incident in the first half of the 2-2 draw went unpunished by referee Andrew Madley but the FA have now acted retrospectively using video evidence, Gallagher accepting a charge of violent conduct.
The suspension means the 34-year-old will miss the Championship games against Norwich and Derby and the League Cup tie at Leeds.
He will be available again when Bolton visit Deepdale on September 1.
The incident with Allen came just after the half hour, the Welsh international being left with a cut to the nose.
Both sets of players clashed in the immediate aftermath but with no action coming from Madley, Gallagher went on to open the scoring from the penalty spot shortly after.
Stoke boss Gary Rowett was damning in his assessment post-match.
“It’s pretty obvious,” he said.
“I’ve watched it again. It’s a blatant elbow.
“He catches him and it’s very, very dangerous and Joe is fortunate it’s only his nose.”
Preston boss Alex Neil on the other hand insisted that there was no malice in the incident.
"Gally said at half-time 'I did catch him gaffer, I didn't mean it. I put my hand up to protect myself and as he turned I have caught him in the side of the face',” Neil said.
"People will have a look at it and make their own judgement but I know the character of Paul Gallagher and know he won't go out with the intention of hurting anyone."