ALBUQUERQUE, N.M. (Reuters) - U.S. border authorities have suspended the processing of undocumented immigrants at a center in New Mexico after one of the detainees was diagnosed with chicken pox, a spokeswoman for Immigration and Customs Enforcement said on Wednesday.

The case was discovered earlier this week at the Federal Law Enforcement Training Center in Artesia, where more than 600 people are being held for processing after entering the United States illegally, said ICE spokeswoman Gillian Christensen.

"The individual is being treated by medical professionals and the necessary precautions are being taken to protect the other detainees at the center," Christensen said.

The decision to suspend processing was taken immediately after the illness came to light, she added.

The center in Artesia began receiving immigrants earlier this month during a surge of arrivals across the southern U.S. border, many of them youths from Central America.

The inflow put pressure on border and customs authorities in Texas, leading the federal government to transport many of the immigrants to centers such as the one in Artesia for processing.

In some areas, plans to house the new arrivals have prompted street protests by critics who accuse the Obama administration of failing to secure the border.

Christensen said ICE was not releasing the age or gender of the chicken pox patient in Artesia, but added the individual had been separated from the other detainees at the facility, which is also home to the Border Patrol Academy.

On admission to such centers, the spokeswoman added, all detainees are evaluated by medical personnel for infectious diseases, uncontrolled mental disorders, or any other condition that could deteriorate if not immediately cared for.

No date has been set for processing to resume, she said.

New Mexico Republican Representative Steve Pearce said the outbreak of the illness could put a strain on Artesia's limited resources, and that his office had communicated its fears to officials at the Department of Homeland Security.

"I am increasingly concerned for the health and safety of the women and children at FLETC (the center) and for the local community," Pearce said in a statement.