Angelica Alvarez remained hospitalized two days after she was found unconscious with the children in the basement of their home, police Capt. Steven Mock said.
He did not give any details on what caused the deaths of the two girls and two boys, ages 2 to 8. Autopsies determined they died of asphyxia.
Mock said Alvarez, 27, was in custody at Elkhart General Hospital. He would not give details on her injuries, but said she was expected to survive.
"I know she's improving," he said.
Alvarez's husband found her and the four children — Jennifer Lopez, 8, Gonzalo Lopez, 6, Daniel Valdez, 4, and Jessica Valdez, 2 — when he returned home Tuesday night. The four children were pronounced dead at the scene.
Martha Williams, who lives behind the family's home, said she did not know Alvarez well, but that she often saw the kids playing outside, riding their bikes and tricycles on the sidewalk, and that they would wave and say hello.
"They were nice little kids, and well behaved, it seemed," she said. "I think most people are still in shock that the kids are gone."
Alvarez was hospitalized in critical condition Wednesday, but Mock said Thursday he did not know an updated condition. A hospital spokeswoman said she could not give out any information.
Mock would only say during a brief news conference that detectives made the decision to arrest Alvarez after an extensive investigation.
"Details, including physical evidence, leading to this probable cause arrest will not be answered," he said.
Bill Wargo, chief investigator for the Elkhart County prosecutor's office, said a magistrate was expected to review the case on Friday to determine whether investigators had probable cause to keep Alvarez in custody.
The prosecutor's office would then have until Wednesday to decide on formal charges, he said. He said he expects his office will seek to keep the probable cause affidavit police will file in support of the arrest sealed until a formal hearing is held.
After Alvarez's husband, Fernando Valdez, found the bodies, he ran out into the street and yelled for someone to call police, authorities said. Police officers at first thought Alvarez was also dead, but later discovered she had a faint pulse.
Records of calls made to police from the home show custody disputes between Alvarez and Gonzalo Lopez, her ex-husband and the father of the two oldest children, police said.
Arnulfo Maciel, Valdez's supervisor at Continental Industries Inc., said Valdez left work recently to take his wife to the hospital, where she stayed for a few days.
"He's been leaving work early because of problems with his wife, so he could be with his children, and that's what he was worried about the past month or so," Maciel told South Bend television station WSBT. The Associated Press left a message Thursday for Maciel at the company.
People mourning the children's deaths stopped regularly outside the home to leave flowers, stuffed animals and notes on Wednesday and Thursday.
Michelle Garcia crouched in the rain Thursday, before Alvarez's arrest, as she carefully placed a light brown teddy bear in a pile of stuffed animals, ceramic angels and other items.
A tearful Garcia, a surgical technician at the nearby Elkhart General Hospital, said she didn't know the family but felt she needed to pay her respects.
"I have nieces and nephews and this is just so sad," Garcia said, breaking into tears. "You hear things like that on the news, but you don't expect something like that to happen here. I just wanted to show my respect and show I care."
One boy left a written note wrapped in plastic that read: "We love you. You will all be deeply missed. May you all rest in peace. Love, Brock Crockom and Family."
On Wednesday, classmates of Jennifer and Gonzalo at Woodland Elementary turned their empty desks into memorials with drawings, poems, flowers and teddy bears. On Thursday, the school returned to its normal schedule, said Jodee Shaw, spokeswoman for Elkhart Community Schools.
"After everything settles down, we'll probably be doing some sort of memorial, a balloon launch or something like that," she said. "Today, they're trying to get back to normal."
Williams, the family's neighbor, said the recent days had been tragic.
"Those little ones didn't ask for anything like that," she said. "The father — he's going to have to come home to an empty house. I don't blame him if he doesn't stay here. Who could live in a house where four kids are gone?"