Information about 2,743 individuals was sent to 77 people in an email attachment by mistake last month, the authority said.
The details included names, addresses and birthdates of the adopted children.
The council blamed the data breach on "human error", adding it had taken steps to contact all those involved.
The Information Commissioner's Office (ICO) is investigating and has the power to levy a fine of up to £500,000.
In a statement, the council said: "On 15 June 2017, an employee in the council's adoption team accidentally attached an internal spreadsheet to emails inviting adoptive parents to the council's annual adoption summer party.
"The email and attachment were sent to 77 people.
"This attachment contained personal details relating to 2,743 individuals, comprising current and former adoptees, parents and social workers who had been involved with these families.
"The spreadsheet included personal information such as names, addresses and the birthdates of the adopted children."
A helpline for those who think they may have been affected has been set up and relevant regulators informed.
A review of data protection across the authority has also been launched.
It is understood the member of staff who sent the email no longer works for the council.
Director of People, Ewen Weir, said: "I am truly sorry for the distress caused to all those affected.
"We will work closely with the affected families and individuals to support them at this trying time.
"This breach appears to have been caused by human error and a failure to follow established procedures.
"We are conducting a thorough review of our processes to identify what changes we can make to ensure that this never happens again."
Anyone involved with Newcastle's Adoption Service who has concerns has been asked to call the council's dedicated helpline on (0191) 211 5562.
The details of thousands of children and their adoptive parents were leaked in a party invitation sent out by Newcastle City Council.