The backer of a Silicon Valley autonomous car developer called Zoox said the secretive startup raised a fresh round of capital valuing it at more than $1 billion, roughly equal to a similar company General Motors Co. acquired earlier this month.

Zoox executives have been tight-lipped, saying little in public about the Palo Alto, Calif., company’s plans. The firm is developing technology similar to Alphabet Inc.’s Google car project and Cruise Automation, which GM purchased in a deal valuing it at more than $1 billion, according...