The salary cap is not set yet, but the tag for safeties is believed to be around $10.5 million. The Broncos announced last week they were tagging safety Justin Simmons.
The Jets last used the franchise tag on defensive end Muhammad Wilkerson in 2016.
It buys the Jets time to work out a long-term deal with Maye, giving them until July 15.
General Manager Joe Douglas told reporters at a press conference last week that he has had “productive conversations” about a new deal with Maye’s camp.
Maye, who turns 28 on Tuesday, made 88 tackles, two interceptions, two forced fumbles, two sacks and 11 pass breakups last season.
The Jets made him a second-round pick in 2017.