Police say they tried to pull over the driver of a white pickup truck over but the man sped off, leading them on a short chase. The pursuit ended with gunfire.
The driver died at the scene. His name has not been released and investigators are not saying why officers shot him.
A major crimes task force made up of several Napa County police agencies is conducting the investigation.
This is the sixth deadly officer-involved shooting in the Bay Area this month.
On March 1 in Guerneville officers shot and killed an attempted kidnapping suspect.
There were three fatal officer-involved on March 2 in San Francisco, San Jose, and Union City. One that took place the next day involved Hayward police.