"Russell is deeply embarrassed and the club regret the incident occurred," Warriors chief executive Wayne Scurrah said. "We will investigate it properly and respond to the NRL."
Packer apologised for his actions on Twitter.
"Hey guys just a quick apology to you and your family regarding my accident last night it has offended some which i am sorry it was an unfortunate thing that happened i hope this apology eases your mind somewhat and helps you move on from it as i will be doing thanks russ," (sic) he tweeted.
Former Manly prop Don McKinnon was famously fined $1000 for also urinating on the Lang Park pitch in 1988.
Packer crossed over for his first try of the season last night, one of the Warriors' 10 tries, as his side eased to their fourth win of 2013.