U.S. auto-safety regulators are investigating what is believed to be the first fatal crash involving a Tesla Motors Inc. car that was driving itself, an incident that is likely to ratchet up scrutiny of a technology that has been evolving with little oversight.

Joshua Brown, a 40-year-old Ohio owner of a Tesla Model S, died when his electric car drove under the trailer of an 18-wheel truck on a highway in Williston, Fla., on May 7, according to regulators and a Florida Highway Patrol report. Mr. Brown had earlier in the...