He is serving a sentence at the Midlands Prison where he was arrested today.
Gardai have until tomorrow to continue questioning the 64-year-old suspect.
It’s understood detectives came across the suspect during a cold case review.
Mary disappeared on March 18, 1977 whilst visiting grandparents at Cashelard.
From Kincasslagh, her disappearance is Ireland’s longest running case of its kind.
Gardai have issued a new appeal for information tonight in the case as they continue to question the suspect at Mullingar Garda Station.
Speaking today, Assistant Commissioner Northern Region Kieran Kenny said: “We are appealing for anyone with any information on the circumstances around Mary’s disappearance to contact us. Even something that people may have thought was insignificant at the time could help us advance the continuing investigation.”
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.
A Family Liaison Officer has been continuously liaising with Mary’s mother, Ann Boyle, to keep her informed of developments including today’s arrest.