9:30 AM PT -- Josh Klinghoffer's attorney, Andrew Brettler, tells TMZ ... "It was a tragic accident. After Josh struck this pedestrian in the intersection, he immediately pulled over, stopped the car, called 911 and waited until police and the ambulance arrived. Obviously, he's cooperating with the police throughout the traffic investigation. This was purely a tragic accident."

Former Red Hot Chili Peppers guitarist Josh Klinghoffer is being sued for wrongful death and for allegedly being behind the wheel of a car that ran over and killed a pedestrian.

According to a new lawsuit, obtained by TMZ, Josh was driving a black GMC Yukon in Alhambra, CA back in March when he made a left turn and ran into a pedestrian who was using a crosswalk.

The suit says the pedestrian, 47-year-old Israel Sanchez, was dragged across the asphalt as a result of the collision and sustained blunt force trauma to his head, injuries that ultimately killed him only hours later.

TMZ also obtained video of the alleged incident ... showing a man crossing a street in the crosswalk when he's run over from behind by a black SUV making a left turn. The suit says Josh was driving the car and didn't so much as tap his brakes. He's also accused of being distracted behind the wheel.

The video shows the driver pulling over after hitting the pedestrian, walking over to the body and then turning around and quickly walking back to the car.

The suit says police in L.A. have NOT made any arrests in the case.

Josh played guitar for the Red Hot Chili Peppers from 2009 to 2019 and was inducted along with the band into the Rock and Roll Hall of Fame in 2012, when he was then the youngest inductee ever.

JK ultimately left the RHCP and has been a touring member for Pearl Jam and Jane's Addiction ... and he's said to be on tour with Pearl Jam right now.

He's being sued for negligence and wrongful death ... and the man's family is going after him for damages.

We reached out to Josh's camp ... so far no word back.