Lungisa and three other people, also arrested, have been allegedly defrauding the arts and culture department for the Nelson Mandela Sports Day, the Hawks said on Friday.
"It relates to R2.5-million paid by the department of arts and culture for the Nelson Mandela Sports Day concert," spokesperson Paul Ramaloko said.
Lungisa and the three other people were alleged to have shared the money among themselves.
Ramaloko said Lungisa handed himself over and was subsequently arrested.
The four allegedly lied to the department and promised that they would have R Kelly perform.
At the time of the concert, the department said it had entered into negotiations with the promoter of the R&B singer's recent tour to South Africa.
'We will get our money back'
It was subsequently announced that the star was on the bill for the music concert that would follow the day's sporting events.
However, it was discovered that R Kelly's management had been unaware of the agreement, and he had departed the country as planned.
Ramaloko said all four were expected to appear in the Commercial Crime Court in Johannesburg on Friday.
Meanwhile, the arts and culture department said on August 15 that it would get back its money paid for R Kelly to perform.
"We will get our money back," arts and culture department spokesperson Mack Lewele said on Thursday.
Sport and Recreation Minister Fikile Mbalula in August said a few individuals, who he did not name, wanted to get rich "in a split of a second" by lying to the department.
"This was a scheme by people who wanted to get rich quickly," he told reporters during a briefing at FNB Stadium about the inaugural Nelson Mandela Sport and Culture Day.
"I do not think R Kelly would have shunned performing for Madiba … but he will not be here. The show will continue with the rest of the line-up."
In December 2010 the NYDA organised the 17th World Festival of Youth and Students. The R106-million event was marred by promised events that did not happen.
Later it transpired that artists were billed for the festival but had not even been approached to perform, just as ministers who were billed as speakers. Amounts totalling R250 000 were spent on party supplies like balloons and confetti but there was a shortage of food.
Nevertheless then-chairperson Andile Lungisa spoke of "a resounding success".