Aetna Inc. became the last of the five major national health insurers to project a loss on Affordable Care Act plans for 2016, and the company said it would re-evaluate its participation in the business and cancel a planned expansion.

Aetna, which had previously expressed relative optimism about the ACA’s exchanges, said it now expected a loss of more than $300 million for the year on its ACA plans amid mounting medical costs. The move, coming after a similar shift in tone last week by Anthem Inc., is the latest sign of instability...