"Let Madiba be your inspiration, his spirit must drive you to achieve greater targets regardless of the odds being stacked against you," Jordaan said while visiting the team at their training camp in Johannesburg on Tuesday.
"Tomorrow you have a special responsibility, so go out there and enjoy yourself. It should be a spectacular day."
Jordaan said Wednesday's encounter with Brazil had lots of symbolic significance.
"We want to wish Brazil well in hosting the 2014 Fifa World Cup, in addition to us celebrating 20 years of our cherished democracy.
"This match is also a tribute to (former South African president) Nelson Mandela.
"The two teams will be unveiling their respective new kit.
"Brazil will unveil their 2014 FIFA World Cup playing kit, and Bafana will showcase their new Nike limited edition gear."
The SAFA president said the match was also part of the association's goal of attaining the 2022 vision, which was to see Bafana Bafana consistently ranked among the top three on the African continent and top 20 in the world.
Kick-off for the international friendly is 19:00 at the FNB Stadium.