The Kiwis were ruled two overs short of the target when time allowances were considered by match referee Andy Pycroft.
Captain Kane Williamson accepted a fine of 40 percent of his match fee, while his players received a fine of 20 percent.
"If there is a second minor over-rate offence committed by New Zealand during the event with Williamson as captain, he will be suspended for one match," the ICC said in a statement.
New Zealand suffered an 87 run defeat by hosts England, who became the fisrt country to reach the semi-finals, and have yet to win in this year's tournament.
They can still reach the semis if they beat Bangladesh in their final game and Australia lose to England.