“Two of the clinics are completely shut down after severe structural damage,” spokesman Tebogo Lekgethwane said in a statement.
The closed clinics were Stilfontein Clinic and Parkstreet Clinic in Klerksdorp town.
The third clinic was under the administration of a mine in Stilfontein.
Lekgethwane said renovations had started on the mining clinic and it was expected to be functional by Wednesday.
“As a temporary measure the department has arranged to ferry patients to nearby health facilities through the use of shuttle buses,” he said.
Health MEC Magome Masike would visit the clinics on Wednesday to assess the extent of the damage caused by the earthquake.
The quake, one of South Africa’s largest magnitude earthquakes in the past decade, was felt as far way as Mozambique and Botswana.
The Council for Geoscience said its epicentre was in the Orkney region in North West province, where one person was killed.
ER24 spokeswoman Luyanda Majija said the body of a 31-year-old man was found in an old mining village in Orkney following the quake.
At least 400 houses in the area were reportedly destroyed, premier Supra Mahumapelo told reporters.