Oil Minister Awad Ahmad al-Jaz presented the written directive in a meeting with senior executives of the GNPOC joint operating company and Petrodar, the ministry said.
It orders them "to stop the process of transportation and exporting South Sudanese oil within 60 days starting from Sunday, June 9," the ministry said.
On Sunday, Khartoum froze nine security and economic pacts with South Sudan, including a deal to restore oil shipments through the Red Sea export terminal.
A day earlier, Bashir had said the oil minister must issue a formal order effective Sunday to close the pipeline.
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A source close to the industry confirmed on Tuesday that companies had been given the order, although he said it came verbally.
"There is no written order," the source said, adding that the firms are obliged to act on the verbal directive.
Despite these moves, Khartoum said it remained committed to good relations if the South Sudan government ended what it claims is support for rebels on Sudanese soil.
On Tuesday, the oil minister told the companies that "South Sudan is not serious about implementing the security agreement."
The United States said that, if carried out, Sudan's order to shut the pipeline would be a violation of the nine accords signed in September.
The pacts "only allow for a shutdown with 60 days of notice for economic or technical reasons. This is neither," State Department spokeswoman Jen Psaki said on Monday.
South Sudanese President Salva Kiir urged his people to remain calm and said on Monday he would not take his nation back to war despite Khartoum's "aggressive attitude."
Petrodar is a Chinese-Malaysian joint venture with Khartoum.