Ms Hanson-Young posted a tweet she received from a supporter of Mr Christensen saying they hoped he had "left one in the chamber" to fire directly into her groin.
Writing on Twitter, Queensland Police said that they are aware of the photograph as well as the circumstances behind it. "Preliminary enquiries would indicate that no offence has been committed", the statement read.
"George Christensen is the thug here".
"I think we agree on that and he's taken it down", he told 3AW radio.
It prompted the leader of the Greens, Richard Di Natale, and another environmental activist to refer the photo to police.
George Christensen put up the image showing him in a shooting stance with the comment 'You gotta ask yourself, do you feel lucky, greenie punks?'.More news: Oxfam and Save the Children bosses face grilling from MPs
Mr Christensen went on to say that he saw no problem with the timing of the post, despite the recent shooting in the United States, as it had nothing to do "with the situation in Australia". Political opponents accused Mr Christensen of inciting violence.
"The concern here is that George Christensen has given licence to people to behave in a way that is violent towards other people who may have a different view", he said.
The uproar is the latest headache for the ruling Liberal-National coalition, with Turnbull last week publicly criticising Nationals leader Barnaby Joyce for his affair with a younger former staffer who is now pregnant with his child.
But he conceded it was an off-colour attempt at humour.
Mr Pennings said he'd added Mr Cristensen's post to a complaint he filed on Thursday with Queensland police after receiving over 100 death threats online.
"It was a pretty sexist one and a threat to shoot me", she said.
Labor has also called for Mr Christensen to apologise.