Molewa died on Saturday in a Pretoria hospital, aged 61, after a brief illness, according to initial reports of her death.
"Our sister passed away yesterday, 22 September 2018, following complications of Legionnaires' disease," the minister's brother Fana Mmethi said in a statement issued on behalf of his family on Sunday.
Mmethi said that his sister’s loved ones were finding it difficult to accept her death "given that she was cut down in the prime of her life when she still had so much to offer to her family, her friends, her colleagues, her church, and to her community."
He said the support and messages of condolences from South Africans – and others across the globe – were much appreciated.
The family has yet to announce the late minister’s funeral programme.