A second detainee has died after being shot at a Dallas Immigration and Customs Enforcement field office last week, according to the League of United Latin American Citizens.

Miguel Ángel García-Hernández, 32, was gravely wounded in Wednesday's shooting and has now died from his injuries after being removed from life support, LULAC said.

"Miguel was a good man, a loving father, and the provider for our family," his wife, Stephany Gauffeny, said in a statement released by LULAC.

"His death is a senseless tragedy that has left our family shattered," she said. "I do not know how to explain to our children that their father is gone."

The other victim killed in the shooting, Norlan Guzmán-Fuentes, 37, had been pronounced dead shortly after the incident, LULAC said.

The shooting unfolded on Wednesday morning when a sniper opened fire "indiscriminately" at the ICE building and an ICE van, striking three detainees, authorities said. The suspect, Joshua Jahn -- who died from a self-inflicted gunshot wound after the shooting -- was allegedly targeting ICE agents, not detainees, officials said, citing notes the suspect left behind.

This is a developing story. Please check back for updates.

ABC News’ Luke Barr and Deena Zaru Pettiford contributed to this report.