The 54-year-old actor said his comments did not "come out as intended" and was only meant to amuse, reported People magazine.
"I apologise for the bad joke I attempted last night in poor taste about President Trump. It did not come out as intended, and I intended no malice. I was only trying to amuse, not to harm anyone," Depp said in a statement.
The actor's joke, what could be a reference to the assassination of Abraham Lincoln by John Wilkes Booth in 1865, was made during an appearance at the Glastonbury Festival.
Shortly after news broke of Depp's comments, the White House issued a statement strongly condemning the joke and calling on others in Hollywood to speak out.
"President Trump has condemned violence in all forms and it's sad that others like Johnny Depp have not followed his lead. I hope that some of Mr Depp's colleagues will speak out against this type of rhetoric as strongly as they would if his comments were directed to a Democrat elected official," the statement read.