A court in Cape Town last month ruled the government had failed to allow adequate public consultation for preliminary agreements with Russia, South Korea and the United States for the construction of eight reactors.
Struggling to meet growing electricity demand, South Africa in recent years has also signed agreements with France and China.
"I have decided that I will not be appealing the decision of the Western Cape High Court on this matter," said Kubayi at a press conference.
The government now plans to sign new agreements with all five countries which will then be submitted to parliament, she said.
The government says the planned eight new reactors would supply an additional 9,600 MW of electricity, more than five times current nuclear output.
But the cost of about one trillion rand (USD 73 billion), announced in 2010, has drawn criticism.
The issue turned political, with President Jacob Zuma and his backers pushing for the programme's development while others, including members of the opposition, are less supportive.
According to several analysts, the respected former finance minister Pravin Gordhan, seen as a bulwark against corruption, was ousted from the government in March because he opposed the nuclear plans.
Uncertainty over financing for the nuclear project was also cited by ratings agencies as one of the reasons behind a downgrade of the country's credit rating in April.