The 50 Rock actor was severely injured June 7 when the limo bus he was riding in was slammed into from behind by a Walmart tractor trailer on the New Jersey Turnpike.
His friend and fellow comedian, James McNair, died.
Morgan was hospitalized with his injuries until June 20, when he was moved into a rehabilitation center.
He accuses Walmart of negligence, saying the driver of the truck, 35-year-old Kevin Roper, was overtired after being awake for 24 hours.
The lawsuit accuses Roper of falling asleep behind the wheel.
The National Transportation Safety Board said the Walmart truck was going 20 mph over the speed limit and Roper was nearly at his drive time limit.
Roper pleaded not guilty to vehicular homicide four days after the accident.
Morgan is seeking a jury trial, and punitive and compensatory damages.