The Bayern Munich player is to remain part of the squad despite hurting his left hamstring in Saturday's 6-1 rout of Hungary in a friendly in Amsterdam.
"We had an ideal (World Cup) warm up until the injury," Van Marwijk told Reuters. "But ... I'm willing to take the risk of keeping Robben in my squad.
"In the past such an injury would take four to six weeks (to clear) but the methods nowadays have developed."
"I will do all I can to get fit in time," he told reporters after having treatment in Rotterdam. "I am very hopeful and now we have to see how we can speed up the process.
"I am almost sure I will travel to South Africa but right now I can't say if that will be in four days or a week.
"I'm glad he (Van Marwijk) gave me time to recover and did not call in a replacement," added Robben.
"Everyone was very down after it happened because he is an important player in our team," said Van Persie after training in Johannesburg. "With his own style and qualities Arjen has something others don't have."
Captain Giovanni van Bronckhorst echoed Van Persie's comments.
"It is normal that everyone is affected if you see how close this team is," said Van Bronckhorst. "But it can also make us stronger.
"That is something we have been working on, the mental part, for two years now."
