Amnesty International said on Friday the closure of the Alina tent camp would force refugees to return to neighbouring war-torn Chechnya without security guarantees.
It is estimated there are 12,000 Chechen refugees living in tent camps in Ingushetia who have fled fighting between Russian troops and resistance fighters in their homeland.
Amnesty said it had received credible reports of intimidation and harassment of refugees in connection with previous camp closures.
According to the United Nations High Commissioner for Refugees, 103 families from the Alina camp want to be relocated to another camp in Ingushetia, while 72 families plan to return to Chechnya.
Amnesty said it had urged the Russian authorities to ensure none of the refugees were coerced into returning to an unsafe environment.
Putin launched the second
Chechen war in 1999
The organisation also urged Moscow to guarantee appropriate accommodation and provide official registration to families who choose to return to Chechnya and those who remain in Ingushetia.
Chechen refugees have been fleeing to Ingushetia since Russian troops poured into Chechnya in October 1999.
The republic had won de facto independence from Russia after a 1994-96 war, but was invaded a second time after President Vladimir Putin came to power.
The official Russian military toll from the second war is estimated at up to 5000 soldiers, although rights groups believe the figure may be closer to 12,000.
Russia says that up to 15,000 Chechen rebels have also been killed, although the official civilian toll has never been published.