Yemen’s Houthi rebels struck Saudi Arabia’s Shaybah oil field, one of the kingdom’s largest, Saudi officials and the Houthis said, deepening tensions between Iran and its rivals that have engulfed the region’s energy facilities.

The Houthis said in a statement Saturday that they had targeted Shaybah with 10 drones. The Iran-aligned rebels said the attack was their largest of its kind on Saudi Arabia, which they have been fighting for control in Yemen since 2014.

The...