"The Jet2 meme has spread a lot of joy and humour around the world but the White House video shows that Trump has neither," she added.
Responding to the clip, Glynne said on Instagram that her music "is about love, unity and spreading positivity - never about division or hate".
The White House post on X was captioned: "When ICE books you a one-way Jet2 holiday to deportation. Nothing beats it!"
It has been met by some with criticism - one user said the clip was "embarrassing and unprofessional", while another said that it "shows a real lack of humanity".
Others have praised Trump for his stance on immigration.
It's not the first time the Trump administration has posted memes on its social media account.
Earlier this month, an image with the president's face superimposed on Superman's face was shared on the account with the caption: "Truth. Justice. The American Way. Superman Trump."
A few weeks ago the administration posted on X saying: "Nowhere in the constitution does it say we can't post banger memes."
President Trump has recently committed $170bn for border and immigration enforcement, including $45bn for detention. ICE, a federal law enforcement agency, will see its funding grow by $76.5bn over five years.