Henicke will start the regular season on the non-football injury list, Andrew Krammer of the Star Tribune reports.
Heinicke was originally given a timetable of three months for a return when he had surgery to repair a torn tendon in his ankle. Placement on the NFI list to start the season means that he'll miss at least the first six games, which he likely would've anyway.
Vannett (ankle) is listed as questionable for Sunday's game in New York, Curtis Crabtree of Sports Radio KJR reports.
Vannett returned to practice Wednesday after an extended absence, and while he's clearly making progress, his NFL debut may have to wait another week. However, he could serve as the No. 2 tight end if he suits up, as Jimmy Graham (back/knee) is also listed as questionable.