Police Minister Fikile Mbalula said the robbery undermined South Africa as a tourism destination.
He told ambassador Gerards: "We don't have words to express our embarrassment and our regret for what happened to the people of the Netherlands."
Mbalula met the Dutch tourists on Tuesday afternoon.
Police spokesman Brigadier Vishnu Naidoo said no arrests had been made.
The Southern Africa Tourism Services Association expressed concern that the attack would harm the industry.
"It is not good for our image," Satsa's CEO David Frost said. "Exactly what impact it will have [on tourism] we don't know. It is clearly not going to have a positive impact.
"What was good is that there was a very co-ordinated response from South African Tourism, and many of Satsa members, to sort the issue out as quickly as we could.
"When an incident like this occurs we have to use it as a learning opportunity," said Frost. "The important thing is that we all need to sit down with the minister and his top team to sort out pre-emptive measures and operating procedures that will prevent these things from happening again."
According to Stats SA, the Netherlands ranked ninth on the list of countries of tourists visiting South Africa in mid-2017.
Stats SA will release its new figures on Thursday.
- Additional reporting by Penwell Dlamini