At least 34 people were killed when police opened fire at the Marikana mine, north-west of Johannesburg.
A further 10 people, including two police officers, were killed in earlier clashes at the mine.
Earlier the owners of the mine, Lonmin, gave their striking workers a final ultimatum to return to work.
In a statement, Mr Zuma said the nation was in "shock and pain".
"We must this week reflect on the sanctity of human life and the right to life," he said.
At least 78 people were injured in the violence and some 250 people were arrested.
Flags will fly at half mast at all flag stations in South African and missions outside the country during the mourning period, which will last from Monday until next Sunday.
On Saturday, former ANC youth leader Julius Malema called on Mr Zuma to resign over the clashes.
Lonmin, the world's third largest platinum producer, said the miners must be back at work by Monday or risk being dismissed.
"The final ultimatum provides RDOs [rock drill operators] with a last opportunity to return to work or face possible dismissal," spokeswoman Gillian Findlay said on Sunday, according to Agence France Presse.