Rapoport reports Martin has a torn labrum and other damage in his shoulder.
New Orleans also placed LB Colton Jumper on injured reserve as well, per Herbie Teope.
Martin, 27, originally signed on with the Chiefs as an undrafted free agent out of Columbia back in 2013. After two years with the Chiefs, Martin caught on with the Buccaneers during the 2015 season but was unfortunately waived with an injury designation later cut loose from injured reserve with a settlement.
The Colts eventually signed him to their practice squad but lost him to the Jets in November of 2015. Martin signed a two-year, $3.8 million contract with the Jets last year and stands to make a base salary of $1.65 million for the 2018 season.
Martin signed a one-year deal with the Saints for the 2019 season after leaving the Jets in free agency.
In 2018, Martin appeared in one game and recorded one tackle for the Jets.