At least 35 people were also injured at the camp, which is housing about 650 people mostly from Niger and Mali, in Ouargla, 800km (500 miles) south-east of the capital, Algiers.
The cause of the fire, that began at about 02:00 GMT, is being investigated.
A Red Crescent official told the AFP news agency that it was believed an electrical fault was to blame.
"A short circuit triggered the explosion of a heater and the fire," Saida Benhabiles said.
Twenty-seven people were still receiving treatment in hospital, she added.
The nationalities of those who died is not yet known.
Many African migrants head to Algeria, using it as transit stop as they attempt to reach Europe.
Numbers have increased since Libya plunged into chaos following the 2011 uprising that toppled long-term leader Col Muammar Gaddafi.
A fire has killed at least 18 people in a camp for African migrants in Algeria, the emergency services have said.