Newry and Mourne District councillors voted last year to retain the name of The Raymond McCreesh Park, sparking outrage from unionist politicians.
South Armagh man McCreesh was a convicted IRA member who had been jailed during the Troubles for offenses including attempted murder.
He died in the Maze prison in 1981 after spending 61 days on hunger strike.
The commission said its investigation will consider whether the council failed to comply with equality guidelines in deciding to keep the name, which was first adopted in 2001.
A statement explained: "The investigation will consider whether, in making its decision, the council has failed to comply with commitments made in its Equality Scheme: namely to have due regard to the need to promote equality of opportunity across the nine equality groups, and to have regard to the desirability of promoting good relations between persons of different religious belief, political opinion or racial group.
"After consideration by its statutory duties investigation committee, the Commission is satisfied that it would be appropriate to have a belief that such a failure may have occurred in this instance. This is not a determination of whether or not such a failure has in fact occurred."
It is understood the investigation could take several months to complete.
A spokeswoman from Newry and Mourne District Council said: "Newry and Mourne District Council can confirm it has received correspondence from the Equality Commission for Northern Ireland advising the commission has authorised an investigation of failure to comply with an approved quality scheme under Section 75, Schedule 9, Paragraph 11 of the Northern Ireland Act 1998.
"As stated within our approved equality scheme, the council will co-operate fully with the investigation by the Equality Commission."
Ulster Unionist MLA Danny Kennedy said he was delighted at the Equality Commission decision to investigate the chosen name, which he claimed had damaged community relations.
"I said at the time that I honestly could not think of anyone less deserving of commemoration in any shape or form - let alone a children's playpark - than Raymond McCreesh, and that those who voted for this should hang their heads in shame.
"I look forward to a speedy investigation and am confident the Commission will find that the decision taken by Sinn Fein and the SDLP in December was clearly wrong and that those councillors be held to account and take responsibility for their actions," he added.