Mulder last pitched in the majors in 2008 for St. Louis. The 36-year-old left-hander was hoping to make the Angels' rotation after being invited in January to spring training, but team spokesman Eric Kay said Mulder felt a pop during agility drills.
Mulder will wait for the swelling to go down before surgery is scheduled. He then faces a six- to eight-month recovery, meaning his career could be over.
"I can handle this," Mulder wrote on Twitter. "But seeing my son in tears when he saw me in a boot and crutches and I told him I wasn't going to pitch. That was tough."
Mulder won 103 games over nine major league seasons with Oakland and St. Louis, including a 21-win season in 2001. He struggled with arm injuries and had surgery over his final two campaigns with the Cardinals, throwing his most recent major league pitch on July 9, 2008.
Mulder had been working as a television analyst and was trying to make a comeback after retooling his delivery.
He sounded optimistic that he would make the team when pitchers and catchers reported on Friday.
"I've worked hard and what I'm doing right now is good," Mulder said. "I know it's working and I'm excited for the opportunity."
Now, a career that was derailed by two shoulder operations could be finished for good after this injury.
Mulder's best season was his second in 2001, when he went 21-8 with a 3.45 ERA while anchoring a dominant rotation with Barry Zito and Tim Hudson. He followed that up by winning 19, 15 and 17 games for Oakland the next three years and then going 16-8 for St. Louis in 2005. But his career got derailed after that. He made just 26 starts and won six games from 2006-08, posting a 7.73 ERA during that time.