Zuma dumped respected finance minister Nhlanhla Nene on Wednesday leading to media speculation that he was protecting the chairwoman of the national airline, Dudu Myeni, to whom he is said to be "close".
Just days before he was sacked, Nene had slapped down a controversial move by Myeni to renegotiate a South African Airways plane-leasing deal with Airbus- a move which analysts said would hit the loss-making airline's finances hard.
Zuma's statement said that Myeni's "relationship with the President is purely professional".
"Rumours about a romance and a child are baseless and are designed to cast aspersions on the president."
Zuma(74), who has four wives, has a reputation as a womaniser and his sexual activities have been scrutinised in public previously, when he was acquitted on a rape charge in 2006.
He became president in 2009.
Nene was replaced by David van Rooyen, a little-known figure from the ruling African National Congress (ANC) party, in a move greeted with dismay by investors and financial analysts.
