Delaney has broken the metatarsal bone in his foot and a scan has confirmed the broken bone.
The Welsh international defender limped-off during Wales' 2-0 win in Azerbaijan on Wednesday evening.
“This is a big blow for us and for the lad,” Villa boss Graham Taylor said.
“From his point of view, it is very disappointing after such a great night for Wales. As far as Villa are concerned, this has denied us the services of a reliable and important player.”