The right-hander has an elbow injury, and the Angels will shut him down, the Los Angeles Times reported.
"We don't anticipate it will be something that will set him back for an appreciable part of the season, but we're going to take it slow," Angels manager Mike Scioscia said, according to the newspaper. "We're going to get a better read as we move along, but from where we are now to the start of the season, it's going to be a stretch."
Santana underwent an MRI, but the results were not immediately available.
Santana felt elbow tightness after one inning of an intrasquad game on Tuesday. On Sunday, he said that "Everything is good," according to the newspaper, but he still will likely not be ready for the opener.
Santana, who signed a four-year, $30 million contract at the start of camp, went 16-7 last season with a 3.49 ERA. He finished sixth in balloting for the Cy Young Award. He struggled in his only start of the postseason, a Game 2 loss to the Boston Red Sox in the American League Division Series.