The 38-year-old, who was jailed for life last week for the brutal murder of two-year-old Santina Cawley, is currently being housed in a single occupancy cell on the prison's E-wing.
The only other inmate on the women's wing housed under such restrictive conditions for her own protection currently is Barbie Kardashian.
Kardashian, who was born male but who identifies as female, was found guilty of seven counts of threatening to kill or cause serious harm to her mother earlier this month.
Sources say child killer Harrington - who was on Covid-19-related quarantine for the first five days of her sentence - is likely to remain on 21-hour- lockdown for the immediate future.
"Harrington is going to be extremely unpopular for what she has done - for the time being anyway," a source told the Sunday World.
"And for the time being, management and operations will err on the side of caution.
"She'll be let out by a prison officer for exercise, to meet with governors and for showers and visits - until such time as the level of threat she is under is deemed to be low."
Asked about the level of threat Harrington would be under as a result of her crime, the source said the main risk is that she might get 'a kicking' or a 'few slaps.'
"Female inmates are different to male inmates," he said, "when it comes to carrying out extremely violent attacks or using weapons like a shiv on other inmates.
"Someone might get a hiding but it would rarely go beyond that.
"There is also the fact that she is still denying what she did to that child.
"If she continues to do so, it will eventually gain her a certain amount of space with her fellow inmates.
"And as the years go by she will become just another face in the prison.
"They'll start looking at her for how she is on the inside rather than what she did on the outside.
"That's not minimising the level of risk she is under or saying what she has done isn't particularly bad.
"It might be decided to keep her on a protection regime for a year, or two years, or even longer.
"Or, it could be decided that it might be safer for her to move her to the Dochas.
"Staff won't make that decision; it will come down from operations."
Harrington will count among her fellow inmates some of the country most high-profile female inmates in the Irish prison system.
These include Scissors Sister Charlotte Mulhall, IRA killer Rose Lynch and Kinahan cartel kill-team member Regina Keogh.
Harrington was sentenced to the mandatory life sentence on Monday after being convicted of little Santina at an apartment in Limerick almost three years ago.
Santina was found by her father naked and critically injured on the floor of Karen Harrington's apartment at Elderwood Park on Cork's Boreenmanna Road in the early hours of July 5, 2019.
She was rushed to hospital, but died there four hours later, in the arms of her mother, Bridget.
She had suffered a severe brain injury and trauma to her body inflicted by blunt force.
Among the injuries recorded by pathologist Dr Margaret Bolster was a complex fracture of the skull in addition to fractures to her right arm and the end of her lower thigh bone, and two fractures to the ribs.
In her evidence, Karen Harrington accepted she was alone with Santina for more than two hours after the child's father, Michael Cawley, left and walked into Cork city centre.
She said she did not murder Santina Cawley but could not say who did.
Ms Harrington's Counsel, Brendan Grehan, in his closing statement, said she had consistently denied she was responsible, and there was no onus on her to prove who was.