Allen is out with a foot injury that was still being evaluated.
But Anderson's injury appears to be more severe. Coach Chuck Pagano said he had a "significant" pectoral muscle injury and early indications were that he may need season-ending surgery.
Both were Colts draft picks in 2012.
Last year, Allen, a third-round pick, was the NFL's receptions leader among rookie tight ends with 45. He broke Ken Dilger's franchise rookie record, too.
Anderson, a seventh-round pick started last season on the PUP list, was cut in November and then re-signed to the Colts' practice squad.