Since the White House announced its zero tolerance policy in early May, more than 2,300 children have been taken from their parents at the U.S. -Mexico border, resulting in a new influx of young children requiring government care.
He called the Trump administration policies "cruel and inhumane".
The policy has also been fiercely criticised by other Central American nations, including El Salvador and Honduras, and global organisations - the UN Children's Fund (Unicef).
American allies in Europe and Latin America on Tuesday blasted as cruel and immoral the Trump administration's policy of separating migrant children from their parents, warned against long-term psychological damage to the children and vowed to work through their consular networks to swiftly reunite families.
"We are working to release the girl, so she can reunite with her father", who is a legal USA resident, Mr. Videgaray added.
However, Pompeo also made clear in his statement that the United States will look to other countries and organizations to play a bigger role in addressing the global migration crisis as the Trump administration changes its approach to both refugees - who apply for resettlement from overseas - and asylum seekers, such as those who enter along the southern USA border after traveling from Central America. Mexico recognizes and fully respects the sovereignty of the United States and its full faculty to decide its immigration policy.
"This is a clear violation of human rights and puts children, including those with disabilities, in a vulnerable situation", Videgaray told a news conference in Mexico City.
He said the girl and her brother were sent to a USA facility in McAllen, Texas, while her mother went to one an hour away in Brownsville.
Her father, a legal US resident, was seeking that the girl be reunited with him, the foreign secretary said.
Of some 1,995 cases registered by U.S. authorities, only around one percent of the children affected were Mexican, and most had already been repatriated, Videgaray said.
Of those separated children, 25 boys and girls are Mexican, said the Videgaray. Indeed some recent detainees are infants, taken from their mothers.
Most of the Mexican minors have already been repatriated and reconnected with relatives in Mexico, but seven remain in US government detention centers, including a small girl with Downs Syndrome, and consular personnel are "attending" to her case, he said.
Mexican authorities were working to achieve the reunification of all of the families involved.
The Trump administration is coming under fire for its treatment of asylum seekers along the southern border with Mexico and continues to reduce the number of refugees it accepts into the United States every year. The note expressed its condemnation and rejection of the "zero tolerance" policy.
On Tuesday, Trump once again tried to blame Democrats for the family separation crisis and took a swipe at Mexico as well. Customs and Border Protection field chiefs over all nine southwest border districts can use their discretion over how young is too young, officials said. In the border town of Tijuana, a dozen migrant families interviewed by Reuters said they would try their luck, despite the risks.
Akemi Vargas, 8, cries as she talks about being separated from her father during an immigration family separation protest in front of the Sandra Day O'Connor U.S. District Court building in Phoenix.
An unapologetic President Donald Trump defended his administration's border-protection policies Monday in the face of rising national outrage over the forced separation of migrant children from their parents.
The current Mexican presidential campaign has elicited comments in support of Mexican immigrants in the United States from all the major candidates.