The private group was called "I'm 10-15" and had about 9,500 members, including former and current Border Patrol agents, the American nonprofit organization ProPublica reported.
Some posts mocked migrant deaths, while others targeted Latino members of Congress, ProPublica said.
The Border Patrol chief has called the posts "completely inappropriate".
"Any employees found to have violated our standards of conduct will be held accountable," Carla Provost said.
According to ProPublica, members of the group mocked Latino members of Congress who visited migrant detention centers in Texas on Monday.
Democrats Alexandria Ocasio-Cortez and Veronica Escobar were among those said to be targeted, with members calling them "hoes and scum buckets".
In one post, a member reportedly suggested throwing burritos at them.
The BBC was not able to independently verify the existence of the private group, which is not publicly accessible on Facebook.
Matthew Klein, an assistant commissioner at the Customs and Border Protection (CBP), said the Department of Homeland Security (DHS) has launched an investigation into the group, which violated the agency's code of conduct.
He said a number of CBP agents may be members of the group, without elaborating on their roles.
Ocasio-Cortez said the posts did not surprise her, saying it was "indicative" of what she saw while visiting migrant detention centers on Monday.
On Twitter, she claimed that Border Patrol officers had told women in cells to "drink out of the toilets".
"I see why CBP officers were being so physically and sexually threatening toward me," she tweeted after the trip.
The CBP has not officially responded to her comments.
However, a DHS official, who spoke on condition of anonymity, told The Washington Post that drinking water was available, and no border agent would force migrants to drink from a toilet.
Ocasio-Cortez and other lawmakers toured detention centers days after a harrowing picture of a drowned man and his daughter in the Rio Grande brought the migration crisis into sharp focus.
Since taking office in 2017, US President Donald Trump had adopted tougher policies in an attempt to reduce the number of undocumented migrants.
Earlier this month, Mexico reached a deal with the Trump administration to try to stem the flow of undocumented migrants travelling to the US.
Since then, deportations and detentions of undocumented migrants have reportedly increased.
In February, Trump declared an emergency on the country's southern border, saying it was necessary to tackle what he said was a crisis there.
Last week, the US Congress approved a $4.5 billion (£3.5bn) humanitarian aid package for the US-Mexico border.
The above article was taken from the BBC.