A community vote on the proposed nuclear waste dump on South Australia's Eyre Peninsula has been delayed after an Aboriginal group won a court injunction.

Key points: The Federal Government has shortlisted Kimba for Australia's future nuclear waste dump

The Federal Government has shortlisted Kimba for Australia's future nuclear waste dump The Barngarla Aboriginal people have won an injunction to halt a community vote

The Barngarla Aboriginal people have won an injunction to halt a community vote The Supreme Court will hear the case next Thursday

The Barngarla people, the traditional owners of much of the Eyre Peninsula, applied for an injunction to halt the vote in South Australia's Supreme Court, arguing it contravened the Racial Discrimination Act 1975.

Lawyers for the Aboriginal group argued the District Council of Kimba did not have the power to conduct the postal ballot, which was due to begin on Monday.

The Federal Government has shortlisted two sites near Kimba as possible locations for a low to medium-level radioactive waste storage facility, along with another site near Hawker in the Flinders Ranges

The lawyer representing the Barngarla Determination Aboriginal Corporation, Daniel O'Gorman SC, told the court his clients had no issue with the vote going ahead, they just wanted to be included in it.

"That's all they want, they just want to be included, they don't want to be treated any differently because their rights are Aboriginal rights," he said.

"There is no justification for excluding people on the basis of native title rights."

The court heard the majority of the 211 native title holders lived outside the boundary of the Kimba District Council and that excluding them from the vote had the effect "of nullifying or impairing their rights".

But Michael Burnett, representing the District Council of Kimba, told the court its power to conduct the postal vote came from the Local Government Act.

He said the council wanted to conduct the vote in a fair manner and decided the fairest manner was to comply with "the statutory procedure that applies in the case of elections".

"It's not a vote that has direct consequences … it's part of a range of consultations that will be taken into account," he said.

Mr Burnett said there were direct consultations taking place with native title holders about the proposed sites, a claim which Mr O'Gorman rejected.

"They're getting two bites of the cherry and therein lies the exclusion, [the native title holders are] only getting one," Mr O'Gorman said.

Mr Burnett questioned why the Barngarla Determination Aboriginal Corporation had waited until August to seek an injunction when they had known about the vote since May.

But Mr O'Gorman said the corporation had written to the District Council of Kimba on six occasions seeking to be included in the postal vote and council had only made its final decision on July 27.

The vote of around 800 residents who live in Kimba will be delayed until after a full court hearing next Thursday.