This breach of the ICC code of conduct was deemed to be of the Level 1 variety, which carries a minimum penalty of an official reprimand, a maximum penalty of 50 per cent of a player's match fee, and one or two demerit points.
Southee has since admitted his offence to an ICC judicial panel and has been handed one demerit point - his first for over two years.
When a player reaches four or more demerit points within a 24-month period, they are converted into suspension points and a player is banned.
Two suspension points equate to a ban from one Test or two ODIs or two T20Is, whatever comes first for the player.
While Southee has performed relatively well with the ball in the two sides' series so far, taking four wickets for 126 runs, the Black Caps have stumbled to two straight losses this week.
The series will now be decided on Sunday in Wellington in a match that begins at midday.