The chief executive Cameron George has confirmed the 20-year-old second-rower will miss Saturday's game in Auckland as punishment for what he described as a "low-range" offence.
George didn't give a date for the incident, which doesn't appear to have attracted a police charge.
"We expect better from our players and anyone who falls short of our standards will be appropriately dealt with irrespective of the time of year or their standing within the club," George said in a statement.
"Isaiah is extremely remorseful for his actions. He feels like he's let his teammates, the club, our fans and his family down.
"He is now determined to win back their respect and will also be fighting hard to earn back his spot in the team."
Coach Stephen Kearney confirmed Papali'i will be available for their round-two match against Wests Tigers in Sydney.
Kearney didn't want to comment further on the offence.
"It's a club issue, that's the issue and that's all I will say on it," Kearney said.
"Sometimes its a challenge for our young men but certainly the headlines across the Tasman, the severity, is something we're dead set against at this footy club,"
"Like everyone we want to get on with playing."
Papali'i was present at the training session.