Malik's appearance in the match has received widespread coverage and sparked a debate in the media.
"We have not issued any notice to Malik to explain his position nor do we intend to do so in future as he has gone to India on a private visit and played in just a club match," a board official said.
He, however, conceded that when Malik returns home the board would have a discussion with him about such future forays into Indian club cricket.
Malik is among the players who have been given central contracts by the board for 2012.
Reports in the Indian media have quoted senior Board of Control for Cricket in India officials expressing their surprise as even the Delhi and Districts Cricket Association ( DDCA) did not inform the BCCI about Malik's participation.
According to the reports, apart from the IPL, the BCCI does not allow foreign players to feature in domestic tournaments.
Another PCB official said since Malik had played in a club match it could not be considered as a domestic game.
Malik is married to Indian tennis star Sania Mirza and frequently visits India. Last year also, while visiting India he played in a couple of club games.
Sources close to Malik said he played in the club match on the request of an Indian friend who is a keen cricket enthusiast.