US President Donald Trump confirmed on Truth Social that Mr Kirk is dead.
Mr Kirk, the CEO and co-founder of the conservative youth organisation Turning Point USA, was shot at an event at a Utah Valley University.
DUP leader Gavin Robinson said: “The tragic murder of Charlie Kirk represents more than violence against one man, but an assault on freedom of speech and open dissent. Our democracy depends on our ability to disagree peacefully.
“Whatever our politics, violence should never replace debate.
“Above all, this is a devastating loss for his loved ones. My thoughts and prayers are with them this evening.”
DUP MLA Jonathan Buckley said, “honestly I’m heartbroken,” describing him as “a wonderful man.”
“A young life cut short by vile, sick and twisted ideology. Praying for Charlie’s family, friends and America.”
Their party colleague, Gary Middleton, added: “Awful news tonight. Praying for Charlie and his family.”
President Donald Trump shakes hands with Charlie Kirk (Manuel Balce Ceneta/AP)
TUV leader Jim Allister KC MP said: “The tragic murder of Charlie Kirk is a profound loss. In today’s interconnected world, he and Turning Point USA are widely known and respected by conservatives far beyond the United States. Our thoughts and prayers are with his family.
“For too long, terms like ‘right-wing extremist’ have been applied unevenly by the press. It is time for all forms of political violence to be recognised and condemned without bias.
“This principle should have been applied consistently after the attempted assassination of President Trump. We hope this tragedy prompts renewed focus on how extremism is reported and addressed by the media.”
Alliance MP Sorcha Eastwood also posted: “The murder of Charlie Kirk is horrifying and chilling. Political violence is wrong. Always. If you can’t condemn it, you are a part of the problem.
“You debase yourself and you destroy any argument you seek to advance. You destroy our basic humanity and empathy. His poor family, my prayers are with them.”
Videos posted to social media show Mr Kirk speaking into a handheld microphone while sitting under a white tent emblazoned with the slogan “The American Comeback” and “Prove Me Wrong”.
A single shot rings out and Mr Kirk can be seen reaching for his neck with his right hand.
Stunned spectators can be heard gasping and screaming before people start to run away.
The Associated Press was able to confirm the videos were taken at the Sorensen Centre courtyard on the Utah Valley University campus, where Mr Kirk was speaking on Wednesday.
Charlie Kirk hands out hats before speaking at Utah Valley University (Tess Crowley/The Deseret News via AP)
Mr Kirk was speaking at a debate hosted by his non-profit political organisation.
The event had been met with divided opinions on campus. An online petition calling for university administrators to bar Mr Kirk from appearing received nearly 1,000 signatures.
The university issued a statement last week citing First Amendment rights and affirming its “commitment to free speech, intellectual inquiry, and constructive dialogue”.
The college said a “single shot” had been fired at Mr Kirk and a suspect was in custody.
Earlier President Trump and a host of Republican elected officials offered prayers for Mr Kirk on social media.
“We must all pray for Charlie Kirk, who has been shot. A great guy from top to bottom. GOD BLESS HIM!” Mr Trump posted on Truth Social.
The shooting comes amid a spike in political violence in the United States across all parts of the ideological spectrum.