The 29-year-old died after she was shot in the head while covering riots in Derry.
In a statement given to The Irish News using a recognised codeword, the group offered “full and sincere apologies” to her family and friends.
Ms McKee was standing next to a police car on the Creggan estate when she was hit as a masked gunman fired towards police on 18 April.
Police believe the violence was orchestrated in response to an earlier search by officers aimed at averting imminent trouble associated with this week’s anniversary of the Easter Rising.
In a short statement, the Police Service of Northern Ireland (PSNI) did not disclose any further details about the nature of the arrest, only that the woman was taken to Musgrave Serious Crime Suite.
Two teenage men initially arrested by detectives investigating the murder were later released without charge.
The New IRA is an amalgam of armed groups opposed to the peace process and it recently claimed responsibility for parcel bombs sent to London and Glasgow in March.
The group said in a statement: “On Thursday night following an incursion on the Creggan by heavily armed British crown forces which provoked rioting, the IRA deployed our volunteers to engage.
“We have instructed our volunteers to take the utmost care in future when engaging the enemy, and put in place measures to help ensure this.
“In the course of attacking the enemy Lyra McKee was tragically killed while standing beside enemy forces.
“The IRA offer our full and sincere apologies to the partner, family and friends of Lyra McKee for her death.”
The admission came as police said the investigation into the killing was continuing at a “rapid pace”.
Detective Superintendent Jason Murphy said more than 140 people had contacted officers with information, adding: “This was an attack on the community. Lyra, tragically, was a random victim and I need the public to continue to support us.
“Many witnesses have contacted us to give us information that has been provided to them.
“More than 140 people have contacted us via our major incident public portal with messages, including mobile phone footage.”
Mr Murphy appealed for witnesses or anyone with information to come forward.
“I want to reassure people that you don’t have to commit to anything today. I just need to speak to people to understand what they know,” he said.