This is according to an oil workers' union and the National Oil Corporation (NOC).
Munier Abu Assoude, head of the oil worker union at Mellitah port complex that is fed by Wafa said Wafa was still open but pipelines to the field were shut. Al-Wafa produces normally around 30,000 barrels per day (bpd) of very light oil condensate.
"Both pipelines have been closed, production in al-Wafa field will be stopped if the protesters do not open the pipeline," he said.
He did not disclose the demands of the protesters, but another official at Mellitah said the shutdown was in protest over the decision by the country's interim congress to extend its mandate beyond the end of its initial term limit.
Protesters also threatened to close a pipeline from El Sharara field in the south, an NOC spokesman said. Negotiations with protesters were ongoing, he said, and the field was still operating at 301,000 bpd.
Losing production at El Sharara which usually produces around 340,000 bpd would be a major blow to Prime Minister Ali Zeidan's government as it tries to end six months of export disruptions in the east of the country.
Armed protesters led by former rebel Ibrahim al-Jathran have seized three key oil ports in the east since August, cutting of around 600,000 barrels per day of export capacity, to demand more regional autonomy.
Oil strikes and pipeline shutdowns by tribes, former rebels and armed protesters are a major challenge for Libya's fragile central government as it tries to restore stability nearly three years after the fall of Muammar Gaddafi.
The fate of the General National Congress is just one of a range of interlacing political disputes in Libya, where a weak central government struggles to overcome political deadlock and the influence of heavily armed former rebels.