Lucy Letby, 28, is in custody, with police searching her home and car in connection with the deaths at Countess of Chester Hospital.
Police said they are investigating the deaths of 17 babies and 15 non-fatal collapses between June 2015 and June 2016.
Ms Letby has been arrested on suspicion of murder in relation to eight of the babies and attempted murder in relation to six of the babies.
It is not known whether the police are investigating any other suspects. Officers were seen searching her home in Chester and plain-clothes officers were seen at her parents' home in Herefordshire
The nurse had worked at the hospital's neonatal unit since graduating from University of Chester in 2011 with a degree in child nursing, and spent time at the unit during her training.
In July 2016, the Countess of Chester Hospital commissioned an independent review of the unit because of concerns about a rise in "unexplained" deaths.
In the same month, the trust also stopped treating the most premature babies, with all those in need of intensive care or high dependency cots sent elsewhere.
But the review, by the Royal College of Paediatricians and Child Health, was unable to explain the deaths, despite the fact consultants noted similarities between the cases.
The report, dated November 2016, highlights a failure to investigate the cases. Although most of the infants underwent a post-mortem, these did not include systemic tests that would have found traces of poisons, or changes in blood sugar levels.
Toxicology tests are not routine, but are often used when a cause of death cannot be established and would show any drugs or chemicals in the system.
The same report notes that "mention of installing CCTV on the unit without explanation had unsettled the nursing team further".
In December, the hospital went further issuing patients and staff with electronic tracking wristbands in a bid to monitor free beds.
An NHS source said Ms Letby was moved into administrative duties in late 2016, saying: "They moved her into admin, they didn't move her to another nursing position.
"If they did think she was suspicious why didn't they suspend her?"
The police investigation was opened in May 2017 after the trust said it continued to be concerned about the unexplained deaths.
It was initially looking at the deaths of 15 babies between June 2015 and June 2016, but has now been expanded to examine 17 deaths and 15 non-fatal collapses.
The number of baby deaths under investigation could make it the largest such scandal in NHS history.
Det Insp Paul Hughes, in charge of the investigation for Cheshire Police, said: "This is a highly complex and very sensitive investigation and, as you can appreciate, we need to ensure we do everything we possibly can to try to establish in detail what has led to these deaths and collapses.
"As a result of our ongoing inquiries we have today arrested a healthcare professional in connection with the investigation.
"While this is a significant step forward, it is important to remember that the investigation is very much active and ongoing."
Ian Harvey, the hospital's medical director, said he was confident the unit was currently operating safely.
He said: "We are continuing to support Cheshire Police with their ongoing investigation. Asking the police to look into this was not something we did lightly, but we need to do everything we can to understand what has happened here and get the answers we and the families so desperately want.
"The Countess is now equivalent to a Level 1 Special Care Baby Unit and we are confident the unit is safe to continue in its current form."