Andrés' ThinkFoodGroup company, which manages his restaurants and other enterprises, called the lawsuit "unsurprising and without merit" in a statement following the lawsuit filed on Friday.
"Simply put, Mr. Trump's comments made ThinkFoodGroup's participation in this project impossible and constituted a breach which the landlord, Trump Old Post Office LLC, refused to remedy," the statement said. "And despite our attempts to negotiate an amicable resolution, we were ultimately forced to terminate the lease."
Andrés backed out of the deal to open a restaurant next year in a new Trump hotel after the presidential candidate and businessman said most Mexican immigrants in the US were criminals.
Andrés was born in Mieres, a town in the province of Asturias in northern Spain. He trained under renowned chef Ferrán Adrià at El Bulli, named the world's best restaurant a record breaking five times before it closed in 2011.
Andrés took US citizenship in 2013 and has often spoken of his pride of being an immigrant in the United States.
"More than half of my team is Hispanic, as well as many of our clients," the chef previously told Spanish newspaper El País.
"And as a proud Spanish immigrant, who recently obtained citizenship, I firmly believe that every human being deserves respect, regardless of immigration status," he added.
Andrés is one of many Trump associates distancing themselves from the real estate magnate since his anti-immigration comments caused a storm of controversy.
"They're bringing drugs. They're bringing crime. They're rapists," Trump said during his campaign launch in June about Mexican immigrants in the United States.
Druggies, drug dealers, rapists and killers are coming across the southern border. When will the U.S. get smart and stop this travesty?— Donald J. Trump (@realDonaldTrump) June 20, 2015
Television channels Univisión and NBC have also decided to cut ties with Trump, announcing they would not broadcast the Miss USA and Miss Universe beauty pageants, co-owned by Trump.
Andrés also recently made headlines when he saved the life of a man choking on a sausage.