Elon Musk’s SpaceX successfully launched a Crew Dragon capsule on its maiden voyage into orbit without people on board, but technical challenges could delay for months the first trip carrying astronauts.

A Falcon 9 rocket blasted off from Florida’s Kennedy Space Center Saturday at 2:49 a.m. local time. The first stage separated in less than three minutes and the second stage put the spacecraft into its initial orbit about eight minutes after that, beginning a historic six-day mission to the international space station intended...