Boss is expected to be out four to six weeks for the procedure, which will clean out debris in his ankle.
Coach Tom Coughlin expects Boss to be back in time for training camp at the start of August.
"The idea was to try to put him into the season without the pain, on a weekly basis-type stuff," Coughlin said.
Boss is not the only Giant who will undergo surgery. Backup offensive lineman Kevin Boothe will be out for approximately four months after tearing a pectoral muscle while working out earlier this week, during the team's organized team activities. He will undergo surgery next week.
Boothe will likely miss most of training camp due to the injury.
Boss injured his ankle against Kansas City during Week 4 and dealt with the injury throughout the season. He missed one game last season, against Oakland, the week after he hurt his ankle.
The tight end rested his ankle after the season was over and felt fine working out while running. However, he aggravated the injury once he began changing directions on it recently.
"I think that was probably the initial blow to the ankle that kind of started it, and the whole season just kept having a couple of tweaks here and there and made it for a long season with my ankle," said Boss, who was able to participate in team offseason drills this week. "Better now than sometime during the season."
Boss and Boothe are the latest Giants to undergo surgery. Several G-Men are on the mend and recovering from offseason surgeries, including running backs Brandon Jacobs (knee), Ahmad Bradshaw (feet and ankle) and Andre Brown (Achilles).
All three were on the field on Friday during the Giants' OTA. Bradshaw is working on a limited basis but said he is feeling good. Jacobs is also ready for a bounce-back season after he and Bradshaw struggled with injuries last year.
"I feel really good," Jacobs said. "I feel better than I did at this time last year."