Dawai received a red card for foul play during the final quarter of his side's 27-5 win against Taieri at Watson Park on Saturday.
He joined a scuffle which involved half a dozen or so players and was sent from the field for striking another player.
Two other players received yellow cards - Harbour's Aleki Morris and Taieri's Karl Still - for their involvement in the incident which happened about 30m away from play.
A red card carries an automatic two-week stand down but Dawai could face further sanction, community rugby manager Richard Perkins said.
''Obviously, we'll get the information in ... and I'd imagine probably a hearing will be called, but that will be up to the judicial panel,'' Perkins said.
If the decision was made to conduct a hearing, it will go ahead sometime this week.
Sanction guidelines suggest a two-week ban is appropriate for an offence at the low end.
A mid-range offence carries a five-week ban while top-end offences begin at eight weeks with a maximum penalty of 52 weeks.
Dawai has been in good form for Harbour with eight tries this season and he will be anxious to avoid further penalty.
The Hawks are unbeaten since round one and their victory against Taieri has positioned them as title favourite.
