Harley-Davidson Inc. has stopped production and deliveries of its first electric motorcycle after discovering a problem related to the vehicle’s charging equipment, a major setback for a product the company is counting on to rejuvenate sales.

The motorcycle maker said it has suspended production of the LiveWire model as it conducts tests to investigate the problem. The company said Monday that the tests were progressing well but didn’t say when production would resume.

Harley...