News of the surgery was first reported by the Cincinnati Enquirer, which said a three-month recovery is anticipated.
Eifert hurt his left ankle late in the Pro Bowl on Jan. 31 and had to wear a boot after the game.
Initial tests went well, and it appeared he would have a quick recovery. He even began participating in the Bengals' voluntary workouts in April. But sources indicated the surgery stems from the injury.
On the play in question, Eifert was trying to snag a throw from Tampa Bay Buccaneers quarterback Jameis Winston in the back of the end zone. Eifert had to stretch out a little for the attempted touchdown throw and his momentum brought him to the ground. Eifert then got up and hobbled to the sideline, where he was initially evaluated.
Eifert was one of several players not in attendance at Tuesday's voluntary practice during organized team activities.
Last month, the Bengals announced they were exercising their fifth-year option on the tight end. That means Eifert, who has another year on his rookie contract, will be in Bengals stripes through the 2017 season.
Eifert was one of the Bengals' most prolific pass-catchers last season. He caught 52 passes, including a team-high 13 touchdowns.