The Thai-built Xayaburi dam, a few hours from the northern Laos town of Luang Prabang, is set to be completed in October, the latest in a welter of barriers across the waterway.
It has been cloaked in controversy since construction began in 2012, with environmentalists raising alarm about its likely impact on the Mekong's fish species, ecosystem and water levels.
The Electricity Generating Authority of Thailand (EGAT) has agreed to buy 95 percent of the electricity generated by the dam once it comes online later this year.
But on Friday activists from Thailand's Mekong provinces issued a petition to the supreme administrative court calling for "an urgent temporary order" to halt EGAT's plans.
The plea comes as northern Thailand is hit by a severe drought due to late monsoon rains and low water levels in the Mekong.
The petition said current river levels in the area were in "critical condition".
"The reduction of water is a result of the storing water to generate electricity by Xayaburi dam," it added.
Last week the Mekong River Commission, an inter-governmental group, said river levels in June and July had dropped to "among the lowest on record".
There was no immediate comment from CH. Karnchang, the Thai company building the Xayaburi dam.
The dam is expected to produce 1,220 megawatts of electricity when it comes fully online in October.
Conservation group WWF has said fish migration and food supplies would be disrupted and has called for the project to be delayed until further impact studies are carried out.
Landlocked and impoverished Laos has ploughed ahead with ambitious dam building projects, setting its sights on becoming "the battery of Asia".
But its Mekong neighbours Vietnam, Thailand and Laos have all raised concerns about the downriver impact of Laos' outsized hydro power ambitions.
The cost of the dam building frenzy was laid bare last year when a massive hydropower project collapsed in southern Laos, submerging large swathes of land and killing dozens.
International Rivers said this month that 5,000 people remain homeless and confined to threadbare camps a year after the disaster.