A 15-man Bangladesh squad left Dhaka on Saturday for the series, which will start with the first Test at Potchefstroom on September 28.
"Some people may think we don't have any chance against South Africa. But I don't agree with them," Mushfiqur told reporters before departure.
"We don't have a very good record in South Africa. Very few us have played in South Africa. It is the kind of place where everybody struggles. Maybe we also have to struggle," he said.
"Personally I think if you don't believe in yourself, you won't get any success. Firstly, we have to believe that it is possible for us to beat South Africa. We did not have this belief even three years ago," he added.
Bangladesh lost all four Tests in South Africa by an innings margin during their previous two visits in 2002 and 2008, but Mushfiqur said they were now in much better shape.
"So we have now got the confidence. Hopefully this series will be a kind of landmark for us. We are ready to take on the challenge.”
"If we can play well in the two Tests overseas that will be a kind of message," he said.
The team, he said, had improved since their two Test matches in New Zealand in January. "Our record in New Zealand was also not good, but we played better cricket this time. We lost both Tests but played much better cricket than the past."
In the weeks after their loss to New Zealand, Bangladesh beat Sri Lanka and Australia in two Test matches away and at home respectively.
"We are in much better shape, an improved team than our last South Africa tour," he said, adding if they did well in South Africa.
Mushfiqur, however, said the absence of star all-rounder Shakib Al Hasan is a setback for the side.
Shakib will sit out two Test matches after asking for a six-month break from Tests.
"You need to play two players in his place, to be honest – one batsman, one bowler... for me as a captain his absence is a kind of setback," he said.
The second Test will be held at Mangaung Oval, Bloemfontein on October 6-10.
Bangladesh will also play three one-day internationals and two Twenty20s in their month-long tour to the African nation.
First Published: September 16, 2017, 7:28 PM IST