The Punjabi Association of South Australia had requested the Campbelltown City Council to grant them permission to hold Indian Diwali festival at Thorndon Park in October.
Last week, at council meeting, this request was rejected.
The association has now accused the local council of discrimination.
ABC reported that the council was about to approve the use of the park for the festival but two councillors vetoed the motion.
Punjabi Association of SA President Kuldip Chugha says their request was rejected on the grounds that the festival would not appeal to the wider community.
"They are saying that if you want to hold a function you have to speak English there," he said.
"They make very discriminatory comments at their council meeting."
Mr Chugha was told that only the local Campbelltown community could hold such events at Thorndon Park.
"We feel like Campbelltown City Council is not welcoming of a multicultural society," he said.
"They are not considering us like we are Australian, like a society that's part of Australian society, they made a comment in such a way that we are like an outsider group."
Previously, the group had organised the Diwali Festival at the same venue in 2014 which had attracted more than 10,000 people from around the state.
"It was attended by Opposition Leader Steven Marshall and local members of Parliament John Gardner and Vincent Tarzia and the Governor of South Australia, so everybody likes it," Mr Chuga said.
"Why do they only have an objection against us?"
The festival organisers will now have to look for another location to host the festival.
SBS Hindi has contacted Campbelltown City Council for a comment and is awaiting their response.
