Malik said his team, Sialkot Stallions, did not chase a modest victory target against Karachi in Lahore on Thursday because they wanted to knock rivals Lahore Eaglets out of the competition.
"We have taken serious notice of this incident and after going through the reports of the match officials we will decide if the matter is to be referred to the disciplinary committee," Pakistan Cricket Board (PCB) Director Saleem Altaf told Reuters on Friday.
Malik has since apologised, saying he had reacted after feeling his team had got a raw deal in an earlier defeat against Lahore.
The 23-year, who has played eight tests and 99 one-day internationals and who was one of Pakistan's successes in the one-day series win in India earlier this month, accepted he had acted immaturely as a captain and player.
"He has apologised and he has been fined by the match referee, but we still feel he acted inappropriately for a Pakistan player," Altaf added.
"The chairman of the board is not happy and we feel he has sent out a wrong message and damaged the tournament."
If the matter is referred to the disciplinary committee, Malik's selection for next month's tour of the West Indies could be in jeopardy.
The country's inaugural Twenty 20 carnival, contested by 11 regional teams, has attracted crowds of up to 12,000 and is seen by the board as a long-overdue boost for the domestic game.
The Karachi, Lahore and Sialkot teams were tied for a place in the next round from one group. Lahore would have qualified if Sialkot had beaten Karachi, which seemed certain with just 20 runs needed in under four overs with seven wickets left.
The Sialkot batsmen, however, including Malik, slowed down, allowing Karachi to win by four runs.