The Cape Times reported that the Agriculture, Forestry and Fisheries department approved the permit, which would allow the nets to be in place until January 2014.
The city's environmental resources head Gregg Oelofse said the nets would be deployed depending on the weather patterns in the next few weeks.
They would be deployed in the morning before sunrise and taken out of the sea at sunset.
Fish Hoek, situated on the False Bay coast, home to both a seal population and a large number of great white sharks.
According to the report, the nets were different to those in place in Kwazulu-Natal, which were designed to trap and kill sharks.
The Fish Hoek nets had a far smaller mesh and were designed to be a barrier rather than a device to kill.