The biggest U.S. meat company wants a cut of the meat-replacement business as well.

Tyson Foods Inc., which slaughtered and processed nearly 2 billion chickens last year, this summer plans to introduce nuggets made from peas, flaxseed and other plants. The new nuggets will compete with patties and sausages made by startups and large food companies vying for a slice of the fast-growing plant-based foods business.

Tyson’s...