"The search was called off 30 minutes ago to allow city engineers to use heavy machinery to remove concrete," Neil Powell of private emergency firm Crisis Medical said.
Powell said the search could resume if signs of life were detected but that after nearly 19 hours into the search hope was fading.
"So far there has been no sign of life, it could be that there are not people there at all or they are trapped beneath the rubble. We don't know."
One person has died and 29 people have been rescued after the vast roof of the structure collapsed on yesterday afternoon in the town of Tongaat.
Chris Botha of private emergency medical firm Netcare 911 said 29 people "were treated and stabilised and they were taken to hospitals, one of them by helicopter."
A woman was found and died at the scene, while others were treated for broken bones, multiple fractures and crush injuries.
Under emergency lighting rescue workers toiled through the night with sniffer dogs and specialist equipment trying to find an unknown number of construction workers who may still be trapped.
Cheap labour means it is not unusual to see hundreds of workers toiling away at construction sites in South Africa and the incident occurred at 4:30 pm (1430 GMT), just as many labourers were knocking off.
Police spokesman Thulani Zwane said officers were trying to interview the contractors and owners to know how many people are missing.
There were earlier suggestions that the toll could be as high as 50. But rescue workers on the scene appear to have significantly revised down that estimate.
The incident happened around 40 kilometres (25 miles) north of the Indian Ocean city of Durban.
Fiona Moonean, who lives across from the building site, was washing dishes when she heard a "thunderous noise" coming from outside.