Teva Pharmaceutical Industries Ltd. is preparing for a potential reckoning with the U.S. epidemic of opioid addiction.

The drugmaking giant said it set aside $646 million to help pay legal expenses related to its alleged role in the abuse of the addictive painkillers linked to tens of thousands American deaths annually. U.S. authorities are seeking steep damages from Teva and a handful of other prominent pharmaceutical companies—three drug distributors offered $10 billion to settle a range of state lawsuits against them, people familiar with the matter told Bloomberg earlier this week.

The provision is the biggest step Teva has taken...