Dlamini said the storm was now heading north, but he could not say with certainty whether the tornado would continue to those areas.
The province has been on high alert since Sunday. Four people have been confirmed dead since torrential rains and wind started battering the province.
Several videos and images of the violent storm surfaced on social media, with some residents reporting that it hit Eskom facilities in the area.
Saws has warned of possible flooding in Limpopo, KZN and Mpumalanga.
Meanwhile, Saws said further showers were expected for the rest of the week and warned that accumulated rainfall for tomorrow and Friday could exceed 100mm and 150mm in some parts of KZN.
The service said this meant "extreme danger to life due to fast-flowing rivers".
The warning comes after torrential rain with thunderstorm hit Blouberg local municipality in the Capricorn district in Limpopo on Friday, affecting more that 400 households.
A husband and wife died when their bedroom collapsed in torrential downpours in Amaoti, Inanda, north of Durban, on Monday.
Aaron Zondo, 68, and his wife Nomathamasanqa Nyangule, 55, were asleep when the incident happened.