Gugu passed away on Monday morning while attempting to reach the summit of Mount Kilimanjaro in Tanzania.
Zulu was one of the climbers on the #Trek4Mandela campaign.
"Details are sketchy. What we do know is that Gugu experienced problems breathing. South Africa is poorer without him", Mbalula said.
"We are all devastated".
He says the exact cause of death is still unclear.
In his last Facebook post, Gugu Zulu on Saturday said, "Am having flu like symptoms and struggling with the mountain but taking it step by step!"
Meanwhile, the Presidency has also sent its condolences to the family of the late Zulu.
"On behalf of the Board and staff of the Nelson Mandela Foundation we extend our honest condolences to his wife Letshego Zulu, their daughter Lelethu and the Zulu family on this tragic loss". "The president is deeply saddened by this event".
In a statement, the foundation said the 38 year old race and rally driver, who appeared regularly on DSTV channel Ignition as track tester for the show Ignition GT, experienced breathing problems while climbing the mountain with his wife Letshego, project leader Richard Mabaso and well-known mountaineer Sibusiso Vilane, while taking part in the Trek4Mandela initiative.
"Gugu was part of the Trek4Mandela team that attempts to summit Kilimanjaro in support of young girls from disadvantaged communities. They are only due to come down the mountain tomorrow, where they will hear of the news".
The two were often referred to as the "adventure couple". He leaves behind his wife and baby girl who turned one in June.
The sports ministry, motorsport enthusiasts and other South Africans have come forward to pay tribute to Zulu, whose been described as a loving, dynamic and unselfish individual.