Dolphins coach Mike McDaniel said Tuesday that Shaheen will undergo surgery after getting more opinions on his knee and the organization is "100% supportive" of his decision.
McDaniel said Shaheen was practicing fine before the trade "with nothing holding him back."
"We 100% thought he was 100% healthy," he said, adding: "We were surprised, as I know Adam was, and that was something that we definitely didn't anticipate."
In the trade, the Dolphins would have acquired a 2023 sixth-round pick from the Texans in exchange for Shaheen and a 2023 seventh-round pick.
Shaheen was battling for a spot on Miami's final roster as the team's fourth tight end. In his five NFL seasons with the Dolphins and Chicago Bears, Shaheen has 50 receptions for 509 yards and seven touchdowns.
Tuesday is the deadline for NFL teams to cut down to 85 players. Besides putting Shaheen on IR, the Dolphins also waived offensive lineman Cole Banwart, wide receiver DeVonte Dedmon and defensive lineman Jordan Williams and waived/injured cornerback Tino Ellis, who will revert to IR if he goes unclaimed on waivers.