He gave no further details of the alleged assault in northern Johannesburg, but said that he would give a full account to President Jacob Zuma and the ruling ANC party.
"His (Manana's) friend said that she must stop taking the video".
A case of assault has been opened with the South African Police Service (SAPS) against the Deputy Minister of Higher Education and Training, Mduduzi Manana, police confirmed on Monday.
It is alleged that Manana slapped her across the fact and assaulted her in the parking lot after that.
Women's minister Susan Shabangu said she received the news of the alleged assault "with great shock". "South Africa must be safe for all women", Zuma said in a statement.
He apologised "unreservedly" to Mandisa Duma, who was reportedly injured, her family, the government and all South Africans, especially women, pledging to "address the harm that has occurred". "I will also meet with my organisation‚ the ANC‚ and President Zuma to give a full account of the incident".
"The deputy minister turned around and slapped Thando and pounced at her and pulled her by her hair, and a friend of his proceeded to assault her by hitting and slapping her as well, while others managed to get me outside the restaurant".More news: Next Apple TV could support 4K, HDR video
"Does it really matter what she said, to a point where she had to be attacked?"
Duma‚ who was accompanied by her female cousin and a friend‚ claimed she was with Manana and his four friends inside the then already closed Cubana in Cedar Square‚ Fourways‚ in the early hours of Sunday morning.
Duma said the case was opened at the Douglasdale police station.
The incident caused a public outcry when an audio clip surfaced on social media.
He has since admitted he was involved in the "shameful incident", saying that "regardless of the extreme provocation, I should have exercised restraint".
"Such behaviour is unacceptable and should be roundly condemned by all in our society". While Manana admits that the incident took place in the recording, he denies that he was responsible.
"The African National Congress calls upon our law enforcement agencies to act without fear or favor to investigate these allegations and bring the perpetrators to book", the ANC said Monday.