The lawsuit was filed by the American Civil Liberties Union (ACLU) and other organizations in the US District Court in California on Thursday.
The policy, known as the Migrant Protection Protocols, was introduced by the Trump administration in December last year.
The policy requires Central American asylum seekers who cross the US-Mexico border to be sent back to Mexico to wait while their requests were being processed.
The process of reviewing the asylum claims is said to take months or years, with a backlog of more than 800,000 cases pending in immigration courts, Presstv reported.
The rights organizations said they had filed the lawsuit on behalf of 11 anonymous asylum seekers, arguing that the program puts asylum seekers in danger and is "in violation of the humanitarian protections to which [migrants] are entitled under United States and international law."
The plaintiffs stressed that the areas where Central American asylum seekers are forced to wait in Mexico are experiencing record levels of violence and are often more violent than the cities they left.
The rights groups also called on a US judge to revoke the policy and order the US administration to bring the migrants back to the country while their cases are processed.
“Both the US and Mexican governments know that the border area is unsafe for women and children,” Michelle Brane, director of the Migrant Rights and Justice program at the Women’s Refugee Commission (WRC), said in a statement.
“The US government knows full well that asylum-seeking families are no threat to this nation,” she added.
Under the direction of US Department of Homeland Security, Customs and Border Protection officers began denying entry to single men late last month and recently started including families with children at the border between Tijuana and San Diego.
The decision to turn back non-Mexican asylum seekers to Mexico came as Trump escalated efforts to severely limit the number of migrants and refugees entering and living in the US.
Thousands of Central American asylum seekers, fleeing poverty and violence in their home countries, reached the US-Mexico border in 2018.
The asylum seekers travel in caravans for protection against Mexican gangs that prey on them en route.
Washington implemented a "zero tolerance" policy to criminally prosecute and jail all undocumented border crosser, even those traveling with their children, leading to a wave of family separations last year.
Trump has made toughening immigration policies a central tenet of his presidency and has vowed to build a wall along the US-Mexico border to curb the flow of migrants from Mexico and Central America despite a record five-week government shutdown triggered by his spat with Congress over funding the barrier.
The US president has already floated the possibility of declaring a national emergency, threatening to do so if Congress did not provide him with $5.7 billion for the wall.