Benabderrahmane also said authorities planned to set up banks in African countries as part of wider economic reforms in the North African OPEC member nation.
Algeria has announced plans to develop its economy and diversify it from oil and gas after a fall in energy earnings caused financial problems.
"Takaful will be available at state companies from next week," Benabderrahmane told state radio.
That step follows a move by state banks last month to start offering Islamic finance products in a bid to attract money from the parallel market, he said.
The government has said sharia-compliant services would help find new funding sources for the economy, which currently relies heavily on oil and gas export revenues.
The authorities have also said they will open the door for the private sector to set up banks, part of reforms pledged by President Abdelmadjid Tebboune in the banking sector.
The next steps include expanding abroad by setting up banks in African countries, mainly in neighboring Niger and Mali, Benabderrahmane said.
"Opening an Algerian bank in Africa has become necessary in order for Algeria to gain access to the African market," he said.