The South African Human Rights Commission (SAHRC) says it is "deeply concerned" by the protests in Johannesburg.
The commission, in a statement on Monday, called for calm.
"Reports emerged over the weekend of these criminal activities and the commission calls for calm and, a respect for and the observance of the rule of law. The commission also notes with concern similar displays of looting, violence and vandalism which erupted in Pretoria last week."
The protests began on Sunday in Malvern, Johannesburg, and spread to Jeppestown, Tembisa and surrounding areas.
News24 reported protesters had burned tyres, hassled bystanders and looted shops believed to be owned by foreign nationals.
The SAHRC has subsequently called on the government and members of the police to restore calm and "end the violence plaguing these communities".
Protesters told News24 they wanted foreigners out of the area, claiming they were dealing drugs.
The SAHRC also called on the community to use alternative channels to voice their concerns that "respect the rule of law".
"The commission urges communities to uphold and respect the rule of law despite their frustrations. Living within a constitutional democracy, with legal and constitutional mechanisms through which we can resolve our concerns, the SAHRC finds it inexcusable for anyone to be subject to the violence so many communities are experiencing at the moment."
It added while it recognised the "social, economic and political factors which give rise to the unrest in South Africa", it has in the past called on role players to deal with these factors that could give rise to violent unrest.
"The commission will soon engage relevant officials and stakeholders in the cities to look into this situation and see how the root causes can best be addressed in order to avoid a repeat of these unfortunate events."
On Monday morning, the police said 41 people had been arrested since the early hours of Sunday.
Gauteng police commissioner Lieutenant General Elias Mawela said the incidents were "inhumane".
"It is a sad day when people choose to capitalise on the misfortune of others to advance anarchy or criminality. Three people perishing in a burning, collapsing building can never justify what is now happening in Jeppestown, Malvern and surrounding areas. With such a tragedy, the community should be uniting to assist those affected instead of seeing an opportunity to commit crime," said Mawela.
The provincial police said officers were "on high alert and monitoring" Reiger Park and Oakmore in Tembisa following several attacks on shops in those areas.