Ngakoue, 27, suffered the injury during Monday's loss to the Los Angeles Chargers but had not been added to the injury report until Friday before quickly going from out to IR on Saturday morning.
He had been a full participant in practice before feeling discomfort in his throat. It was determined that Ngakoue would need a procedure after consulting with a team doctor, according to the Colts.
Ngakoue finishes his first season in Indianapolis with 9.5 sacks and one forced fumble after joining the Colts in a March trade.
In a corresponding move, the Colts signed defensive end Kameron Cline to the 53-man roster from their practice squad.