Democratic state senator Maria Chappelle-Nadal posted the comment on Facebook but later deleted it.
The Secret Service has confirmed they are "looking into the comments" and say "all threats against the President" will be investigated.
The senator says she was wrong to write the post but that she will not resign.
She had written "No. I will. I hope Trump is assassinated!" in response to a comment on Facebook.
She told the St Louis Post-Dispatch: "I didn't mean what I put up. Absolutely not.
"I have deleted it, and it should have been deleted.
"I am not resigning. What I said was wrong, but I am not going to stop talking about what led to that, which is the frustration and anger that many people across America are feeling right now."
Members of her own party were quick to condemn the comment with some calling for her resignation.
The leader of the Democratic Caucus in the Missouri senate, Gina Walsh, said her colleague "should be ashamed of herself for adding her voice to this toxic environment."
US Senator Claire McCaskill, also a Missouri Democrat, said: "I condemn it. It's outrageous. And she should resign."
The Republican Governor of Missouri Eric Greitens added his voice to calls for her to step down.
He said: "We can have differences in our country, but no one should encourage political violence. The senator should resign."
However, Ms Chappelle-Nadal insists she was exercising her right to free speech.
"I refuse to resign for exercising my First Amendment rights, even though what I said was wrong," she said.
A Missouri lawmaker is being investigated by the US Secret Service for saying she hopes President Donald Trump will be assassinated.