According to a report in 7news.com.au, Bairstow was handed one demerit point under the ICC's disciplinary code after a review of the incident, which took place during the tourists' series-clinching Super Over win at Eden Park.
Bairstow was the man of the match for his whirlwind 18-ball 47 where he tonked five sixes and hit two fours.
England on Sunday won the the 5th T20I against New Zealand in Super Over in what turned out to be a thriller of a decider in Auckland to clinch the five-match series 3-2.
New Zealand opted to bat first in the match which was reduced 11 overs a side due to rain and eventually ended up posting an imposing total of 146/5.
Morgan and Bairstow came out to bat for England in the Super Over and scored 17 runs off Tim Southee's bowling.
Jordan then bowled the Super Over for England with Guptill and Tim Seifert in the middle. New Zealand could manage just eight runs in the over after losing the wicket of Seifert.