Tesla Inc. will restructure and flatten its management, Chief Executive Elon Musk told employees Monday, as the Silicon Valley auto maker struggles to boost production of its Model 3 sedan amid an exodus of top leaders

Mr. Musk made the announcement following news that his engineering chief, Doug Field, was taking a leave of absence, and that senior executive Matthew Schwall was leaving the company for Alphabet Inc.’s driverless car division Waymo.

“To...