"Some seven villages home to about 1,300 families and over 6,000 people were under water", the newspaper reports, citing the Attapeu Planning and Investment Department's director, Soulichanh Phonkeo.
United States non-governmental organization International Rivers said the break was caused by ongoing heavy monsoon conditions and heavy rain in Laos.
ABC Laos reported that the water levels were rising in the district but did not provide any more information.
The Xepian-Xe Nam Noy dam project in southeastern Laos has collapsed, displacing hundreds of people in the region.
The dam "was fractured and the water had leaked to the downstream area and down to the Xe-Pian River which is about five kilometres from the dam", said Kijja Sripatthangkura, chief executive officer of Ratchaburi Electricity Generating Holding Company.
The dam was constructed by a joint venture led by South Korean companies, with Thai and Lao partners.
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The dam was being built by the Xe Pian-Xe Namnoy Power Company.
The collapse at the hydroelectric dam in Attapeu province late on Monday sent flash floods through six villages, Lao News Agency said.
The 410 megawatt capacity dam was supposed to start commercial operations by 2019, according to the venture's website.
As well as disquiet within Laos, several neighbouring nations are anxious its ambition to become the "battery of southeast Asia" will disrupt vital ecosystems and their own river systems.
Six Vietnamese workers were killed when a gas cylinder exploded at the construction site of a hydropower plant in central Laos in July a year ago.