Six-year-old Mary of Kincasslagh, Co Donegal, disappeared while visiting her grandmother at Ballyshannon on 18 March, 1977.
The arrest comes after new evidence was discovered by the Review Team based in the Northern Region that has been investigating the disappearance.
The man has been detained for questioning in Mullingar Station under the Criminal Justice Act 1984. He can be detained for up to 24 hours.
Mary was on a family visit to her grandparents’ home with her parents and siblings when she disappeared.
As well as the investigation at the time ,there have been two reviews by An Garda Síochána into Mary’s disappearance.
The latest began in 2011 and is being undertaken by a Review Team from the Northern Region.
The Review Team has conducted what they call “a significant investigation” that has involved interviewing a wide range of people and undertaking a number of searches with the assistance of forensic and geology experts. Its investigation is ongoing.
Anyone with information is asked to contact the Incident Room at Ballyshannon Garda Station at 071 9858530 or the Garda Confidential Line 1800 666 111.
Gardaí say a Family Liaison Officer has been continuously liaising with Mary’s mother, Ann Boyle, to keep her informed of developments including today’s arrest.
In 2011, gardaí released a picture of what they say Mary could look like today.