The Angels announced the decision Thursday in another blow to their injury-plagued lineup.
Heaney entered the season the No. 2 starter after his promising debut with the Angels, who acquired him in a trade in December 2014. He went 6-4 with a 3.49 ERA in 18 starts last season and was named the AL's rookie of the month in July.
Heaney made just one start in April before tearing his ulnar collateral ligament. He hoped to avoid surgery with rest and stem cell therapy, but his elbow wasn't progressing.
Dr. Neal ElAttrache will perform elbow ligament replacement surgery on Heaney on Friday in Los Angeles.