Google’s firing of an engineer over his controversial memo criticizing its diversity policies and “politically correct monoculture” didn’t violate U.S. labor law, a federal agency lawyer concluded.

Statements in James Damore’s 3,000-word memo “regarding biological differences between the sexes were so harmful, discriminatory, and disruptive” that they fell outside protections for collective action in the workplace, an associate general counsel for the National Labor Relations Board wrote in a six-page memo disclosed Thursday.

Damore withdraw his complaint in January and...