The attack sparked a fire in a Saudi gas plant Saturday but caused no casualties or disruption to production, state-owned energy company Saudi Aramco said.
The facilities attacked included a refinery and oil storage, it said.
The Houthis have carried out a spate of cross-border missile and drone attacks targeting Saudi air bases and other facilities in recent months.
Shaybah, which produces about a million barrels of crude oil a day, is located more than 1,000 kilometres from Houthi-controlled territory in northwestern Yemen.
The field sits in the Arabian Peninsula’s Empty Quarter, only a few kilometres from the border with the United Arab Emirates.