No one on board was injured, but a spokesman for the wananga said they were shaken.
"Certainly it's a surprise. It's not something that we've ever experienced so I'd have to agree [that it was random],'' he said.
The organisation was focused on ensuring the well-being of its students, who were being offered victim support.
Some of the students were now back on campus, others were talking to police about what they saw.
The minibus was later towed away.
Police said initial indications were that the weapon was a BB gun and that the occupants of the bus were not specifically targeted.
Witness descriptions of the vehicle were unclear but police wanted to hear from anyone who saw a red or maroon car acting suspiciously in the area or who had any information about the incident.
Anyone with information was urged to contact Otahuhu police on (09) 259 1200 or Crimestoppers anonymously on 0800 555 111.
