The White House added the song in a post of a man with his wrists handcuffed to his waist as he is patted down at an airport. The video was captioned with the song's lyrics: "You don't have to go home but you can't stay here."
"We did not authorise or condone the White House's use of our song in any way. And no, they didn't ask," the power pop trio from Minneapolis said in a statement.
"The song is about joy and possibilities and hope, and they have missed the point entirely."
Asked about the post on Monday, White House press secretary Karoline Leavitt said "our entire government clearly is leaning into the message of this president".
US Customs and Border Protection retweeted the White House's post on X with the caption "It's closing time. We are making America safe again."
Closing Time is from Semisonic's 1998 album, Feeling Strangely Fine, and the song hit No. 4 on Billboard's Adult Alternative Airplay chart and earned a Grammy nomination for best rock song.
The track was written by frontman Dan Wilson, who has previously spoken about its meaning.
In a 2018 interview with Billboard, the musician explained Closing Time was partially inspired by the birth of his daughter, Coco.
Wilson also co-wrote the Grammy Award-winning 2011 Adele track Someone Like You.
Semisonic joins good company in a long list of performers who've objected to Trump using their songs, including ABBA, Bruce Springsteen, Rihanna, Phil Collins, Pharrell, John Fogerty, Neil Young, Eddy Grant, Panic! at the Disco, R.E.M., Guns N' Roses, Celine Dion, Beyoncé and Adele.
- with BANG