McCullers, sidelined for the first 4½ months of last season while rehabbing from a right flexor pronator strain, noticed soreness after a bullpen session last week.
He had an MRI on Tuesday night. He told reporters Wednesday that it showed no structural damage to his elbow but will delay his start.
"I've been a little bit upset,'' he said. "I was really looking forward to a great start to the camp and a great start to the season.''
McCullers, 29, described the injury as a "small muscle strain."
"It will set me back a little bit, but it shouldn't be anything like last year,'' he said. "It should be something where hopefully I'm playing catch in a couple weeks.''
Being ready for Opening Day, he said, "is out of the question.''
"Because of the nature of building up through spring and the number of bullpens you need and then obviously, games, the smartest thing would be to go at a slow pace and then come back and still have the ability to throw the majority of the full season," he said.
McCullers missed the 2019 season following Tommy John surgery. He went 13-5 with a 3.16 ERA in 2021, then was injured in the postseason.
He had signed an $85 million, five-year contract before the 2021 season. McCullers made eight starts from Aug. 13 on last year and was 0-1 in three postseason outings.