They said the children, aged one to 15, had no shoes, were wearing rags and “looked like Third World refugees”.
Five adults were found at the scene, including two heavily armed men.
Police searched the site after receiving a message from a third party that read: “We are starving and need food and water.”
It is not clear how the group ended up at the compound in Amalia, near the state’s border with Colorado.
Police described the compound as a small underground caravan covered by plastic, with no running water or electricity.
Taos County Sheriff Jerry Hogrefe told ABC News the children were hungry, thirsty and filthy.
“I’ve been a cop for 30 years. I’ve never seen anything like this. Unbelievable,” he said.
“They were skinny, their ribs showed, they were in very poor hygiene and very scared.”
No fresh water was found at the site, and the only food there was a few potatoes and a box of rice, police said.
Two armed men, Siraj Wahhaj and Lucas Morton, were arrested at the scene, and charged with several counts of child abuse.
Three women, believed to be the children’s mothers, were detained but later released.
Mr Hogrefe told ABC it appeared the women and children “were brainwashed and feel great intimidation from the men that were in control of this facility”.
The 11 children have been taken into care by local social services.
Mr Wahhaj is also wanted on suspicion of abducting his three-year-old son, but the boy was not among the group found at the compound, US media report. It was the search for the boy that led to the arrests on Friday.
Police said they had been aware of the compound for some time but had to wait for a search warrant to be issued before entering, as the occupants were “most likely heavily armed and considered extremist of the Muslim belief”.
Mr Wahhaj was armed with an AR-15 rifle and four pistols when they encountered him, they said.