President Abdrabuh Mansur Hadi's chief of staff Ahmed Awad bin Mubarak, who was kidnapped on Saturday by the Shiite Huthi militias who control Sanaa, is from the southern province of Shabwa in deeply-tribal Yemen.
"Oil companies in Shabwa will stop production starting midnight if Ahmed Awad bin Mubarak is not released," said the governor, Ahmed Ali Belhaj.
Yemen's only gas terminal of Belhaf, which is located in Shabwa, would also stop operating, he said.
An industry official confirmed to AFP that Shabwa's oil companies had received orders to halt their operations.
Shabwa has three oilfields and produces about 50,000 barrels per day.
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Political sources in Sanaa said Mubarak's kidnap was a bid to press for amendments to Yemen's newly drafted constitution.
It came just before a meeting of the national dialogue secretariat, headed by Mubarak, to present a draft charter that sets out the division of Yemen into a six-region federation, which the Huthis oppose.
Political sources said representatives of the Huthis and former strongman Ali Abdullah Saleh's General People's Congress party walked out of a meeting on the process headed by President Abdrabuh Mansur Hadi on Saturday.
Hadi has been struggling to assert his authority since the Huthis seized Sanaa on September 21.
Mubarak was one of the representatives in the dialogue of the Southern Movement, which seeks autonomy or secession for the formerly independent south.
Since their takeover of Sanaa, the Huthis have pressed their advance into mainly Sunni areas south of Sanaa, where they have met deadly resistance from Sunni tribes as well as Al-Qaeda loyalists.