The accusation was made in an editorial piece called "Migrant Terrorism" in the Church's weekly magazine, From the Faith.
According to a translation from AFP, the editorial accuses Mexican authorities of only making "declarations and promises, their reactions are lukewarm and they also show fear and even worse, submission" to Trump's policies.
The comments come days after the Trump administration issued new orders for a crackdown on illegal immigrants in the US.
There are an estimated 11 million undocumented migrants living in the US, many of whom originate from Mexico.
The new rules will make it easier for immigrant officers to deport illegal immigrants.
The plan would also see the US expel all illegal immigrants crossing the border to Mexico, whether they are Mexican or not.
"What Mr Trump does is not only apply inhuman legalism, but a real act of terror," the editorial said.
Mexico's foreign minister Luis Vdegaray said on Thursday that Mexico would not be willing to accept some of Trump's immigration measures.
"We are not going to accept it because we don't have to accept it," Videgaray said.
"I want to make clear, in the most emphatic way, that the government of Mexico and the Mexican people do not have to accept measures that one government wants to unilaterally impose on another."
Secretary of State Rex Tillerson exits his limousine before his departure to Mexico
US Sectretary of State Rex Tillerson, who visited Mexico last Thursday, said he hoped to work with Mexico to reach an agreement on the immigration plans.
"In a relationship filled with vibrant colours, two strong sovereign countries from time to time will have differences," he said, "We listened closely and carefully to each other as we respectfully and patiently raised our respective concerns."