New Zealand Football spokesman Peter Thornton said the shootings were a "pretty awful situation".
"The team was aware that OFC was managing it, it sounds like the OFC hotel was close to it all."
Mr Thornton said as far as he was aware it was "situation as normal", and he hadn't been told of any increased security measures for the team.
A Ministry of Foreign Affairs and Trade spokesman said no New Zealanders have been involved in the incident, and a safety message has been sent to all 136 New Zealanders registered as being in Papua New Guinea.
"We are advising New Zealanders in Papua New Guinea to exercise a high degree of caution in all parts of Port Moresby, avoid protests and large crowds, monitor local media for updates and follow the instructions of local authorities.
"New Zealanders in PNG should also let family in New Zealand know they're safe and well."
The students had been marching from the university campus to Parliament to demand the resignation of Prime Minister Peter O'Neill over corruption allegations.
Student Gerald Peni told the ABC police fired shots directly into the crowd when students would not let them arrest the president of the student council.
Port Moresby General Hospital said 10 students had been admitted. Thousands of students in Port Moresby have been protesting and boycotting classes for weeks amid growing political unrest.
The Governor of Oro Province, Gary Juffa, a critic of the O'Neill Government, said on Twitter that he had spoken directly with students at the protest. "Informed that several were shot," he said. PNG's opposition made a fourth unsuccessful attempt this week to unseat O'Neill's Government via a no confidence bid.