Brigadier General Yahya Saree made the announcement on Saturday in a televised address carried by al-Masirah satellite news channel.
He said the Yemeni army had sent 10 drones to attack the Abqaiq oil processing facility and the Khurais oil field.
He warned the number of similar attacks against the kingdom would rise if the Saudi-led war against Yemen continued.
“The only option for the Saudi government is to stop attacking us,” he stressed.
Earlier in the day, Saudi Interior Ministry confirmed in a statement that the sites had been "targeted by drones”.
The company describes its Abqaiq oil processing facility in Buqyaq as "the largest crude oil stabilization plant in the world."
Abqaiq, about 60 km (37 miles) southwest of Dhahran in Saudi Arabia’s Eastern Province, contains the world’s largest oil processing plant. Most Saudi oil exported from the Persian Gulf is processed there.