No
Microwaved plastics do not cause cancer.
Can I microwave food in plastic containers or covered in plastic film?
There is no scientific evidence that microwaving food in plastic containers or wrapped in clingfilm can affect the risk of cancer.
—Plastic bottles - Cancer Research UK
Claim: Research has proved that microwaving foods in plastic containers releases cancer-causing agents into the foods.
Status: False.
—Plastic-Tac-Toe - Snopes.com
Myth: Microwaving plastic containers and wraps releases harmful, cancer-causing substances into food.
Fact: Microwave-safe plastic containers and wraps are safe to use in the microwave.
—Cancer causes: Popular myths about the causes of cancer - Mayo Clinic