Coach Adam Gase said Catanzaro, 28, revealed his plans the day after the game.
"He came in Friday morning and told me he was done, he was retiring," Gase said.
On Saturday, the Jets hosted a handful of free-agent kickers, eventually signing Taylor Bertolet. He was on their 2018 training camp roster and played most recently with the Salt Lake City Stallions in the now-defunct Alliance of American Football.
"When I finished my career at Clemson, playing in the NFL was just a dream," Catanzaro wrote on his Instagram account. "After five years in the league, it's time to move on. I can't say I ever thought I would've been a kicker, but I'm thankful that kicking chose me."
Catanzaro's absence Sunday morning at practice prompted some players to think he had been released. He had been on shaky ground, but he received public support from Gase throughout his struggles.
The Jets will continue to explore possible options.
They had a Pro Bowl kicker last season in Jason Myers, but they refused to get into a bidding war when he became a free agent. He wound up signing a four-year, $15.5 million contract with the Seattle Seahawks, who guaranteed $5.5 million in the first year. The Jets thought Catanzaro would be a suitable replacement, giving him a one-year, $2.3 million contract.
Catanzaro kicked well for them in 2017 but left as a free agent to sign with the Tampa Bay Buccaneers. He was released at midseason after missing four PATs and four of 11 field goal attempts. He finished the season with the Carolina Panthers.
By rule, he must return his $500,000 signing bonus to the Jets.
"I appreciate the fact that he came in," Gase said. "He could've easily rode it out, kind of see what happens. I appreciate him doing that at that time and just being straight with me."