Prosecutors accuse the firm of deceptively marketing painkillers and downplaying addiction risks, fuelling a so-called "opioid epidemic".
Johnson & Johnson denies wrongdoing and says it marketed products responsibly.
It is the first of 2,000 cases brought by state, local and tribal governments against pharmaceutical firms in the US.
On average, 130 Americans die from an opioid overdose every day, according to the Centers for Disease Control and Prevention.
