Mrs May said she was "clearly, wholly and unequivocally" clear that she disagreed with the policy.
Speaking to Kay Burley of Sky News, the us ambassador to the United Kingdom confirmed the meeting.
"Meeting Her Majesty is the most important thing, because she's the head of state, and from there on, it'll be what the president wants to do", he said during the interview.
While May has praised the United States for backing Britain's tough stance on Russia after the poisoning of former Russian spy Sergei Skripal, relations between her and Trump have not always been smooth.
In May, Attorney General Jeff Sessions announced a "zero tolerance" approach towards migrants and refugees who cross the United States southern border without documents, promising to prosecute those who did so.
"But we also have some key shared interests with the United States in the security and defense field and on other areas as well".
US President Donald Trump can wager on an uncomfortable reception when he meets Queen Elizabeth during his long-delayed inaugural trip to Britain next month.
Labour MP Gavin Shuker said Mr Trump had locked up 2,000 little children in cages and was refusing to release them until he is allowed to build a wall along the US-Mexico border. Facing domestic and global outrage, Trump issued an executive order Wednesday that ends family separation, instead keeping families together in federal custody while awaiting prosecution for illegal border crossings.
Ms May described images of children in cages as "deeply disturbing".
But Nielsen is on her way to the White House to discuss the issue with the president's team, according to one of the people. She never met Lyndon Johnson.
Despite firm details still being arranged, it is thought that the meeting will take place at Windsor Castle as it will be closed off to the public on July 13.
However, Buckingham Palace have yet to confirm whether it is true. His upcoming visit in July is expected to draw protests.