The video, which has been seen by foxsports.com.au after being circulated on social media, shows Smith wearing sunglasses near what appears to be a white substance on the table of an apartment.
Smith is seen rolling up a banknote and picking up a credit card next to the white substance in the footage, while Munster is standing in the background among at least six people in the hotel room.
Now a second video has emerged of Munster dancing on a table and clutching what appears to be a small package containing white powder in his left hand.
Both The Daily Telegraph and Channel 9 reported the NRL was aware of the first video, with the Integrity Unit subsequently set to ask questions.
When asked by The Daily Telegraph for comment, Storm football boss Frank Ponissi said “there is a process to go through”.
Speaking after being crowned Dally M coach of the year on Monday head coach Craig Bellamy said: “I don’t know the full details yet.
“I’ll make a comment when I know that. I don’t want to be saying something and then it doesn’t turn out to be right.”
Bellamy later added: “Obviously I know of the incident,” he said. “I haven’t spoken to those guys yet in detail.
“It hurts everybody.”
The Storm crashed out of the preliminary finals with a 10-6 loss to the Penrith Panthers on Saturday.
Melbourne finished the NRL regular season on top of the ladder with a 21-3 record, which included 19 consecutive wins between Rounds 4 and 23.