The team was en route to a mosque for Friday prayers at the time of the attack but escaped to the nearby Hagley Oval.
The incident took place around 1.45 local time when the players had gone to pray ahead of the third Test
Neil Wagner ended up with nine wickets and Trent Boult with seven as New Zealand beat Bangladesh by an innings and 12 runs.
Bangladesh were 80 for three, still 141 from making New Zealand bat again.
New Zealand captain Kane Williamson was taken to hospital Monday, for scans on his injured left shoulder.
Bangladesh strike early before rain arrives; The visitors ended up with just 211 on the board.