The vehicle - a Model S with a semi-autonomous driver-assistance system - collided with a Honda Civic in Los Angeles, and two people in the latter died in the crash while the Tesla occupants were treated for minor injuries.
According to the US National Highway Traffic Safety Administration, the car reportedly passed through a red light.
Authorities haven't commented on whether the Tesla's Autopilot played a role in the accident.
The system allows a vehicle to change lanes, self park and navigate autonomously under certain conditions.
However, the Tesla has repeatedly told drivers they must remain alert and not take their hands from the steering wheel even when using the feature.
In a statement, the NHTSA confirmed it has assigned a special crash investigation team to take a look at both the car and the scene of the collision.
The regulator has previously assessed 13 other incidents involving Teslas, with 11 of those still pending.
Meanwhile, several collisions have been blamed on the driver not paying attention rather than the Autopilot system itself.