RIYADH—Saudi Arabia dismissed its long-serving oil minister Ali al-Naimi on Saturday, marking the departure of one of the industry’s most powerful figures, as the country grapples with weak oil prices.

Mr. Naimi, who had been the kingdom’s oil minister since 1995, has been a strong voice against lowering Saudi Arabia’s production when prices fall, a move away from its past tactics. He moved the Organization of the Petroleum Exporting Countries to keep pumping oil at a rapid clip despite a global supply glut, a decision that...