Swarzak was placed on the 10-day DL after straining a muscle on his left side in his second appearance with New York. The team recalled right-hander Hansel Robles from Triple-A Las Vegas before Tuesday night's game against Philadelphia.
"It's really frustrating," Swarzak said.
Swarzak left Saturday's game against St. Louis and was later sent for an MRI. He went on the DL retroactive to Sunday and expects to miss a significant stretch of time.
"A few weeks, from what I understand, is the best-case scenario," he said.
The 32-year-old right-hander was the biggest offseason addition to a bullpen the Mets hope will be much improved this season. The right-hander signed a $14 million, two-year contract after going 6-4 with a 2.33 ERA and 91 strikeouts over 77 1/3 innings in 70 combined games last year with the White Sox and Brewers.
He has given up one run and struck out three in 2 1/3 innings with New York.
"I'm feeling better today than I did yesterday. A step in the right direction," Swarzak said.
Robles was sent to the minors late in spring training. He has been a member of the Mets' bullpen since 2015 but was demoted to Triple-A for almost two months last year, when he finished 7-5 with a 4.92 ERA in 46 major league games.
In other injury-related news, manager Mickey Callaway said Conforto could come off the disabled list this week in Washington. New York begins a three-game series against the NL East rival Nationals on Thursday, the first day Conforto is eligible to be activated.
"He's in a really good spot," Callaway said. "He's getting really close. I think you guys will probably see him very soon."
The center fielder was playing in Triple-A spring training games in Florida, but it appears he won't play in any regular-season rehab games in the minors before coming off the DL.
"Would more at-bats on the minor league side help? Possibly," Conforto said. "But I think at the end of the day, I'm going to have to get my timing back against the (Max) Scherzers and the (Stephen) Strasburgs and the guys I'm going to be facing this year."
Conforto is ahead of schedule in his recovery from surgery for a dislocated left shoulder. The initial target date was May 1.
"I feel very fortunate to be coming back a little bit quicker," he said. "Obviously, I didn't want to miss the first month of the season. May 1 felt a little late to me, so I made it a goal of mine to get back as quickly as possible."
Conforto took swings against new teammate Jason Vargas during a simulated game in the indoor batting cage Monday at Citi Field.
"I feel ready," Conforto said. "I feel good to go."
Vargas threw 65 pitches over four simulated innings Monday, when New York's scheduled game against the Phillies was postponed due to wintry weather. The left-hander is on the 10-day DL following surgery last month for a broken bone in his right hand.
The next step for Vargas, who signed a $16 million, two-year contract with the Mets as a free agent in February, is another simulated game in Florida in four days.