The New Zealand Transport Agency warned a similar failure in an on-road crash could cause serious injury or even death for rear seat passengers.
It said officials encouraged Suzuki New Zealand to urgently address the problem, including considering recalling the cars.
"Whether further regulatory action is required will depend on what steps Suzuki takes to address the issue," it said.
"NZTA is advised that Suzuki NZ has stopped sales of the Suzuki Fronx in New Zealand and is contacting vehicle owners from today to provide them with further information, including advice that passengers do not travel in the rear seats at this time."
Owners who had not heard from Suzuki should contact the company or their local dealers, NZTA said.
There were more than 1115 Fronx vehicles registered in New Zealand.
The Australasian New Car Assessment Programme (ANCAP) gave the car a one-star safety rating due to the seatbelt failure, NZTA said.
"While the seatbelt failure is serious, the low ANCAP rating reflects the vehicle's poor performance across all aspects of ANCAP's testing."
Suzuki New Zealand said a "thorough and disciplined" investigation has begun.
"Suzuki will take any actions required to uphold our safety standards and the trust our customers place in our brand."
The company said it was urgently reviewing the ANCAP testing outcomes "at the highest levels of the organisation" with Suzuki Motor Corporation in Japan and Suzuki Australia.
"Suzuki firmly believes in learning from local testing and regulatory feedback as part of our continuous improvement philosophy.
"These assessments are treated seriously and play an important role in strengthening vehicle safety, performance, and reliability across our markets."
The Fronx was certified as meeting Australia and New Zealand safety standards, it said.
It was released for sale in New Zealand in June this year.
