"Janssen has profited from their illegal conduct, and my office is taking action to make sure they pay for ravaging our communities and destroying our families just to make a profit," Beshear said in a statement.
J&J in a statement said that it marketed and promoted opioids appropriately and that its products' labels provided information about their risks and benefits.
Opioids were involved in more than 42,000 overdose deaths in 2016, according to the U.S. Centers for Disease Control and Prevention.
Hundreds of lawsuits by states, counties and cities have accused drugmakers of pushing addictive pain-killers through deceptive marketing and wholesale distributors of failing to report suspicious drug orders.
Eight other states have sued J&J. Beshear is also pursuing similar cases against drug distributors AmerisourceBergen Corp , Cardinal Health and McKesson Corp and drugmaker Endo International Plc.