Planning to open with a six-man rotation, the team likely will turn to Nick Tropeano, with Parker Bridwell also an option.
Tropeano on Sunday had the best start by an Angels pitcher this spring. He struck out nine Texas Rangers in 5 1/3 scoreless innings.
Because of his previous elbow injury, Heaney made only six starts over the past two seasons. He has started four games this spring, striking out 14 over 11 2/3 innings.
"Anytime a pitcher has a little bump in the road there's some concern," manager Mike Scioscia said. "I think that everything that was evaluated says just that.