The company is conducting tests to investigate the problem in what is seen as a major setback for the motorcycle maker, according to the Wall Street Journal.
The company has not said when production will resume.
Harley was looking to the electric bike to help rejuvenate sales.
The company asked customers and dealers to only use a professional type of charger available at its dealerships rather than electrical outlets at their homes.
The bikes retail for $30,000, are still safe to ride.
LiveWire owners had been able to charge their bikes using their standard wall outlets, although a charge can take 10 hours.
Direct-current charging stations at Harley dealerships can reload the bike’s battery in about an hour, according to the Journal.
Harley is facing an aging problem among its core group of riders, so the company is introducing new models of bikes and looking abroad.
In 2018, 42 percent of Harley bikes went to dealers outside of the U.S.
In July 2018, President Trump scolded Harley-Davidson over the company's overseas production shift in response to U.S. trade policies.