The premier was speaking at a roadblock in Inanda, north of Durban, where 14 people were arrested and a taxi licence suspended.
He said the majority of the arrests were of people who did not have travel permits.
“This will not be for today only; it is going to be carrying on until we are satisfied that all of the people in the district of eThekwini are adhering to the regulations,” he said. “We are also going to be patrolling in townships and in suburbs, because we have established that there are people who are still roaming around and those who are still selling alcohol through back doors.”
Traffic on the N3 entering Durban came to a standstill on Monday as metro police were out in full force checking permits.
Zikalala added that more than 10,000 people had been arrested in the province since the beginning of the lockdown.