Weaver, who has been complaining of tightness in his neck, will miss at least Monday's scheduled spring training start.
Scioscia said the right-handed Weaver, who went 7-12 with a 4.64 ERA in 2015, has already seen team doctors and will get a follow-up examination with a specialist in Phoenix.
"We'll see," Scioscia told reporters. "We're going to meet whatever needs Jered has right now."
In his last outing, Weaver, who is entering his 11th season, topped out at 81 mph and allowed three home runs in 2 2/3 innings against the Dodgers on Wednesday.
A three-time All-Star selection, Weaver led the majors in strikeouts in 2010 and twice has led the American League in wins. He has a 138-81 career record with 1,495 strikeouts and a 3.40 ERA.