The number of U.S. deaths at work from unintentional drug and alcohol overdoses jumped more than 30% in 2016, according to new government data, showing that the nation’s struggle with a deadly opioid epidemic is migrating to the workplace.

The Bureau of Labor Statistics’ National Census of Fatal Occupational Injuries said Tuesday that 217 workers died on the job last year as a result of an unintentional overdose from the nonmedical use of drugs or alcohol, up from 165 in 2015. The number of accidental overdose deaths at work...