Mr Zuma (70), was speaking at a traditional event in KwaZulu-Natal province, his first public appearance since being re-elected president of the African National Congress a week ago.
He described people who love dogs more than humans as "having a lack of humanity", the Durban newspaper the 'Mercury' reported.
Black South Africans should stop adopting the habits of other cultures, Mr Zuma told an audience of thousands on Wednesday:
Some black South Africans responded by posting photographs on Twitter of themselves walking their dogs.
Mr Zuma's office said the message of the speech "was the need not to elevate our love for our animals above our love for other human beings". (© Daily Telegraph, London)