The Brazilians have been drawn in Group F of the competition where they will face Borussia Dortmund, Fluminense and Ulsan.
A total of 32 teams will compete for the prestigious trophy that also includes fellow African sides Al Ahly, Esperance Sportive de Tunis and Wydad Casablanca.
The official trophy was on display at the Mamelodi Sundowns headquarters on Thursday.
Club captain Zwane was at Sundowns when the club competed for the Club World Cup in 2016.
He said on IOL: "It is a very special moment for the whole team. We've been waiting for this moment, and it has come. It's here now!
"Today, we got see the trophy and take pictures with it as well. So, for us, it's just excitement.
"The level was too high (in our last Club World Cup). As a team, we learned a lot, though. I think this time, we are ready."
This year's Club World Cup takes place in the United States between June 14 and July 15.
Golden Arrows coach Manqoba Mngqithi has voiced concern over Mamelodi Sundowns' recruitment strategy, warning that the club's reliance on foreign signings is weakening Bafana Bafana.
Mamelodi Sundowns were held to a 1-1 draw by Siwelele in their Betway Premiership encounter at Dr Petrus Molemela Stadium on Wednesday.
Aubrey Modiba has urged Mamelodi Sundowns to remain focused on the job at hand as they prepare to face Siwelele, while attempting to catch Orlando Pirates.
Mamelodi Sundowns battled to a gritty 0-0 draw against MC Alger in a feisty CAF Champions League showdown on Friday night.
