The poster, which was on display at a GOP event in the West Virginia statehouse, depicts the Twin Towers on fire on 11 September with the words “’Never forget’ – you said” written above the building.
Under the image is a picture of Ms Omar with the words “I am the proof you have forgotten”.
Democratic state lawmaker, Mike Caputo, was enraged by the poster and wanted to get into the chamber to protest.
He admitted to kicking the door during an argument about the image and allegedly injured the security guard, who had to be taken to hospital.
"We have created an anger that I have never witnessed in 23 years in this body and it sickens me. It absolutely sickens me. So yeah, I kicked the door open I'll own it," Mr Caputo said, according to WSAZ.
Ms Omar responded to the offensive image on social media.
— (((Mike Pushkin))) (@pushkinforhouse)
“No wonder why I am on the “Hitlist” of a domestic terrorist and “Assassinate Ilhan Omar” is written on my local gas stations,” she tweeted.
“Look no further, the GOP’s anti-Muslim display likening me to terrorist rocks in the state capitols and no one is condemning them!”
The House Rules Committee is expected to meet to decide if Mr Caputo will face repercussions.