David Pauley was recalled from Triple-A Pawtucket and started against the Angels while utility man Joe Thurston was designated for assignment to make room on the roster. Pauley allowed five runs and seven hits in four-plus innings, taking the no-decision as Boston rallied 7-6.
Beckett (2-1), the majors' only 20-game winner last year, started the season on the 15-day disabled list with a strained lower back before making his first start April 6. Boston manger Terry Francona said after Boston's 7-6 win that Beckett is likely to take his next turn in the rotation.
"My best guess at this point is we'll probably keep him on his next start," Francona said.
Beckett lost his season-opening start April 6 at Toronto, but beat the Yankees in his last two.
Like a number of Red Sox players, Beckett had been suffering from the flu within the past week. Red Sox manager Terry Francona said Beckett was over his bout with the flu, but felt stiffness when he arrived at the Fenway Park.
"He'd been sick as a number of our players are, so we had taken some precautionary measures and pulled David Pauley from his start in Pawtucket in case something happened," Francona said. "Josh thought he was feeling well enough to pitch as far as the sickness went, but then his neck got real stiff and we thought we were putting him in jeopardy by putting him out there."
It was unclear when he would make his next start.
"We just went through the idea that he wouldn't start tonight," Francona said. "We need to get more information and see how he feels. You just don't take a starter and back him up a day. We'll see what happens."
Beckett was unavailable for comment.
Pauley mde his first major league start since 2006. He spent all of last season with Triple-A Pawtucket, going 6-6 with a 4.33 ERA. He was 1-1 with a 1.17 ERA before being recalled.
In 2006, Pauley went 0-2 with a 7.88 ERA in three starts with the Red Sox.
Beckett would have been facing the Angels for the first time since the teams met in last season's American League Division Series, when the right-hander dominated Los Angeles with a complete-game, four-hit shutout in Game 1.
He went on to win his two starts in the league championship series against Cleveland, including winning Game 5 to lead Boston's comeback from a 3-1 deficit, before the Red Sox swept Colorado to win the World Series. Beckett won Game 1, holding the Rockies to one run in seven innings.
Thurston played in four games, going 0-for-8.
Delcarmen changed out of his uniform and into street clothes and went home about an hour before the game started. Varitek, who appeared weak while walking around the clubhouse, was also expected to be out with the flu.
Information from The Associated Press contributed to this report.