News24's editor Adriaan Basson discusses the new digital subscriptions live on Tuesday
He did not say if there had been any arrests.
A video of beachgoers at the upmarket Umdloti Beach, north of Durban, went viral on Monday, showing people fleeing the City's law enforcement officers.
"It must not be perceived or viewed by the public that this is an attempt by government or the City to frustrate them. I think everybody is fully aware of the havoc of Covid-19," Masiyela said of the incident.
He urged the public to continue to abide by regulations.
"Government will not win alone, but it requires that people themselves play a meaningful role in assisting government and the City in flattening the curve of the spread.
"We must also be mindful of the fact that eThekwini is a hotspot in KZN and we must not take that for granted."
Masiyela added: "We are just appealing to the public to be responsible.
"If we continue with this behaviour, we are not going to turn the tide of the coronavirus.
"It's simple, respect regulations, be mindful that we are under lockdown."