Allen injured his ankle in the first half. He was originally listed as questionable to return, then was officially ruled out early in the third quarter.
The Colts believe Allen suffered a high ankle sprain, a source told ESPN NFL Insider Adam Schefter.
The loss of Allen left the Colts without their most versatile tight end. Allen has a team-high seven touchdown receptions this season.
Also hurt Sunday was running back Ahmad Bradshaw, who the Colts fear suffered a broken ankle. Bradshaw will undergo testing on Monday to determine the injury's severity and if surgery is needed, league sources told Schefter.