Ipswich Town have fined midfielder and warned him about his future conduct following his goal celebration in the game against Blackpool on Saturday.
The player has also been asked by the Football Association to explain a celebration in which he appeared to gesture he was wearing a pair of handcuffs in an apparent message of support for a former teammate jailed for a fatal drunken-driving crash.
After scoring the lone goal in a 1-0 win at Blackpool on Saturday, Norris held his wrists together. He later denied he was imitating handcuffs.
Former Plymouth goalkeeper Luke McCormick, Norris' former teammate, was jailed for more than seven years last month after pleading guilty to causing the deaths of two boys by driving drunk while returning home from Norris' wedding.
The boys' mother, Amanda Peak, said that if Norris wanted to send a message to McCormick, he should have done it privately.
"I'm finding it quite hard to deal with everything myself and I'm finding it difficult not to hate Luke McCormick, and when people are doing silly things like that it makes it very hard," Peak said. "If you're going to see Luke in prison, see him in prison, give a phone call. Just don't do something like that in the public eye when there's loads of children watching."
Norris apologized for the message but said it wasn't a handcuffs sign.
"It was a private message but I can see how people might have seen it like that and I apologize if it's caused any offense," Norris said. "Luke is a friend of mine. He made a massive mistake and is paying for that."
The FA said it had written to Norris asking for an explanation.