"A pipeline was found tapped into the main oil pipeline in the Rumaila region," the source said.
"The pipeline stretched across 300 metres under the ground and was equipped with valves and used for contraband," the source added.
General Ali al-Mayahi, who heads the police unit tasked with protecting the south's oil installations, said at least 11 similar pipelines have been found along a 10-kilometre stretch of the Rumaila line.
Iraqi forces and Kurdish fighters have been in a standoff since October 16 along the route of a strategic export pipeline linking oilfields with the Turkish port of Ceyhan.
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The Kurds had stopped pumping oil there before withdrawing, and production is still mostly at a standstill.
To compensate for the losses in the north, Iraq last week said it hiked southern oil production by 200,000 barrels per day.
Last month, Iraq produced more than 97 million barrels of oil.