The England international will be assessed by the club's medical staff after suffering a suspected dislocated joint earlier this week.
"It was an awkward fall. No-one was near him. He fell on his shoulder. It is not always straightforward so we need to go and get it checked out," Sky Sports News quotes Villa boss Paul Lambert as saying.
Delph will miss this Saturday's Premier League clash with Everton, and could also be absent for England's European qualifier against Slovenia next month.