Ali al-Fatimi said Sunday engineers managed to repair damage to the line, which was attacked last week.
Oil deliveries though the pipeline resumed at an undisclosed rate, the official Saba News Agency reported.
Saba said the pipeline was "attacked by saboteurs" but didn't indicate who was responsible.
The Marib provincial leader said local officials and citizens had been able to provide security following the the attack.
Yemen is struggling to control violence amid threats from al-Qaida, southern separatists and northern Shiite rebels.
Energy company Yemen LNG said its facilities at the Balhaf export terminal were attacked by unnamed saboteurs in December.
Al-Qaida took credit for a December attack on the Yemeni Defense Ministry.