Fresno State University in central California said in a statement that Lars Maischak had "agreed upon a voluntary leave of absence".
He tweeted on 18 February: "To save American democracy, Trump must hang. The sooner and the higher, the better."
The FBI and Secret Service have been investigating the posting.
Fresno State president Joseph Castro said in a statement on Tuesday evening: "During his leave of absence, Dr Maischak will no longer have a teaching role, but will be conducting research off campus."
Earlier this month, Mr Maischak wrote in a statement to a news station that he was "appalled that the president of the university is allowing himself to be instrumentalised for a right-wing smear campaign".
The lecturer - who has taught American history at Fresno State since 2006 - said any suggestion he had wished violence against Mr Trump was "far-fetched".
He also defended another tweet that said: "#TheResistance #ethniccleansing Justice = The execution of two Republicans for each deported immigrant."
Mr Maischak's tweet about President Trump - to 28 followers - attracted little notice until it was picked upby the right-wing Breitbart News website.
Breitbart said the lecturer's statements "explain why universities across the country are now viewed with disdain by average, salt-of-the-earth Americans".
Mr Maischak is not the first critic of the president to test the limits of free speech.
The rapper Snoop Dogg fired a toy gun at a Donald Trump character in a recent music video.
Mr Trump tweeted: "Can you imagine what the outcry would be if @SnoopDogg, failing career and all, had aimed and fired the gun at President Obama? Jail time!"
At the women's march in Washington in January, Madonna said she had "thought an awful lot about blowing up the White House".
Newt Gingrich, a prominent Republican and supporter of Mr Trump, said the singer was part of "an emerging left-wing fascism".
A US college lecturer has been placed on paid leave after tweeting that President Donald Trump should be hanged.