The Jets said the 22-year-old will undergo the surgery on Friday.
According to local media reports, he will be sidelined at least three months.
Bogosian set a career best with 25 assists and 30 points in 2011-12 despite missing 17 games. He had 71 penalty minutes and a minus-3 rating, the second best total among the team's regular blue-liners.
Originally selected by the franchise third overall in the 2008 draft, the Massena, N.Y., native is heading into the final season of a two-year pact worth a total of $5 million US.
He has scored 29 goals and 60 assists, with 208 penalty minutes, in 264 regular season games.