Mings is also expected to miss Sunday’s Premier League clash with Burnley as the club continue to wait for a clearer prognosis.
The 32-year-old centre-back was forced off 32 minutes into last weekend’s 3-1 win over Fulham after going over on his ankle.
Mings, who signed a new two-year contract at Villa in the summer, had started all six of their Premier League matches.
His injury means Pau Torres is likely to start on the left-hand side of central defence against both Feyenoord and Burnley.
The Spain international, who has just one Premier League start to his name this term, impressed after replacing Mings off the bench at the weekend.
Asked recently about the competition for places at the back, Torres replied: “Obviously, you want to play every game.
“But at the end when Unai makes his decisions, we need to respect him, his decisions and then just work hard to have one opportunity and then try to play well on the field.
“Everybody works hard in Bodymoor Heath, we want to play every game and that’s it.
“I think this competitiveness between the team-mates is good, it will help the team and we’ll improve our level.”
Villa, who will train at Bodymoor on Wednesday morning before flying to Holland in the afternoon, are aiming to continue their perfect start to the Europa League campaign following last week’s win over Bologna.
Hosts Feyenoord are aiming to bounce back after losing their opening league phase game away to Braga by the same scoreline.