Aisling McCarthy Brady, 34, of Quincy, in a police photo after her Monday arrest.

The Irish nanny accused of injuring and killing a 1-year-old girl is in the country illegally, immigration officials told The Associated Press.

But with her bail set at $500,000 on Tuesday in Cambridge District Court, Aisling McCarthy Brady, 34, of Quincy, isn’t going anywhere.

She was arrested Monday, five days after the death of Rehma Sabir, the child she’d been caring for on Ash Street in West Cambridge. Police say that on Jan. 14 at about 4:41 p.m., they went to her home for a call about an unresponsive infant. The child was breathing but unconscious. Rescue workers took her to Children’s Hospital in Boston, where she was found to be suffering from subdural and retinal hemorrhaging and cerebral swelling. Doctors also saw multiple healing bone fractures. Two days later, the child was pronounced brain dead and died.

Rehma had been alone with Brady “during the time that she sustained injuries consistent with abusive head trauma,” according to the office of Middlesex District Attorney Gerry Leone.

Brady pleaded not guilty Tuesday on a charge of assault and battery on a child causing substantial bodily injury. The district attorney said further charges were expected after a final report by the chief medical examiner.

Defense lawyer Melinda Thompson suggested there could other causes for Rehma’s injuries, though, pointing to the baby’s recent travels to Pakistan, Saudi Arabia and London without Brady.

After hearing the plea, Judge Michele Hogan opted for the high bail and conditions that Brady have no contact with the family of the child; no contact with children under the age of 10; not engage in employment or volunteer work with children; not engage in child care services; surrender her passport; and check in with probation. If Brady posts bail, she is ordered to remain under house arrest with GPS monitoring.

Her next court date is Feb. 22.

Media looking into Brady have found accusations of violence, including restraining orders issued against her in 2005 and March and an arrest in 2007 in which she was accused of beating her roommate. Both women were arrested, though, and the charge against Brady was dismissed.

She arrived from Ireland in 2002 as a tourist allowed to stay up to 90 days, Immigration and Customs Enforcement officials said late Tuesday, meaning she has been living illegally in the United States since. She has advertised for work on sites such as Sitter City and Care.com, but the online nanny and housekeeper services wouldn’t necessarily have known of a criminal record or immigration violations. On Care.com, for instance, families and care providers create profiles and contact each other through them after filtering search results. The site doesn’t employ care providers.

Still, said Nancy Bushkin, vice president of public relations and corporate communications at Care.com, “We are heartbroken by this tragedy and our sincere condolences are with the family during this most difficult time.  We are working with local authorities to assist in any way we can.”