A group of 33 worshippers had joined church rituals on the banks of the Jukskei river when the flooding struck on Saturday, said Robert Mulaudzi, spokesman for the City of Johannesburg Emergency Management Services.
An earlier toll of nine dead rose after the discovery of five more bodies, Mulaudzi said, adding that he could not give a precise figure for the number still missing.
The priest who was presiding at the rituals, including baptisms, survived, Mulaudzi said.
"Two people were swept away and confirmed dead" at the scene on Saturday, while 12 more bodies had since been found, he said.
Rescue workers and firefighters are still searching for missing people, but the emergency services indicated the chances of finding them alive were fading.
Sudden surges of water are common in this part of Johannesburg, where storms take place almost every night during the southern summer.
People have free access to rivers and "practise their religion where they wish," said Mulaudzi.
"But we must intensify our awareness campaigns to avoid such tragedies."