"Welcome to America", reads the headline on the bright red cover ― the newsmagazine's third in as many weeks to feature Trump.
The photo shows the 2-year-old Honduran girl in tears as Border Patrol agents search and detain her mother in McAllen, Texas.
President Trump's Executive Order issued on Wednesday is meant to act as a temporary solution to the issue of child separation, allowing families to remain together while detained and awaiting adjudication.
Video footage of separated children sitting in cages, an audiotape of wailing children and Moore's photo had sparked worldwide anger over Trump's immigration policies.
The original photo was taken by John Moore, a photojournalist for Getty Images who has spent years documenting the border, as well as wars and refugee crises around the world.
"As a father myself, it was very hard for me to see these families detained, knowing that they would soon be split up", Moore told Getty's blog Foto. As the spotlight fell on their faces, their faces exuded a mix of fear and relief.
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Under a moonless sky, a group of Central American asylum seekers is rafted across the Rio Grande from Mexico into the USA on June 12 in McAllen, Texas.
On TIME magazine's cover, the portion of the picture showing the little girl is isolated to create an illustration.
The spotlighted toddler and her mother, whose names have not been released, crossed onto US soil from Mexico last week.
In April, the Trump administration announced its hard-line policy for illegal crossings, saying that any asylum attempt that is not made at an appropriate port of entry would be deemed illegal and the person would be prosecuted even if they had no criminal history.
Moore told Time taking this photo was also been hard not only as a photojournalist but also as a father. "As the border patrol took peoples' names down, I could see a mother holding a young child", Moore said on Weekend Edition Sunday to Lulu Garcia-Navarro. Moore further said that he really wanted to "pick the girl up" at that moment but he couldn't.
Federal prosecutors of at least some detained parents have reportedly not been able to say where their children are being held.