Mr Adams has vehemently rejected allegations made by former republican colleagues that he had a role in ordering the death of mother-of-10 Jean McConville - who was dragged away from her 10 children after being wrongly accused of passing information to the British army in Belfast.
The former West Belfast MP was detained last night after voluntarily presenting himself for interview at a police station in Antrim.
Mrs McConville's son Michael, who was 11 when his mother was murdered, welcomed the arrest.
He said: "We're just happy to see everything moving as it is moving at the minute.
"Me and the rest of my brothers and sisters are just glad to see the PSNI (Police Service of Northern Ireland) doing their job. We didn't think it would ever take place [Mr Adams' arrest], but we are quite glad that it is taking place.
"All we're looking for is justice for our mother. Our mother, on the seventh of next month, would have been 80 years of age.
"Although we didn't spend much time with our mother, we'd have like to have spent a lot of time with her. If the IRA hadn't have killed our mother, God knows, she still might have been alive today."
Sinn Fein deputy leader Mary Lou McDonald said the arrest was "politically motivated" and designed to damage the party and its president.
No-one has ever been charged with the murder of Mrs McConville. But after years without progress in the criminal investigation there have been a series of arrests in recent weeks.
A veteran republican - 77-year-old Ivor Bell - was charged in March with aiding and abetting the murder. Five other people have been detained and questioned.
The recent police activity followed a decision by a US court compelling a Boston university to hand over to the PSNI recorded interviews with republicans about Mrs McConville's murder.
Boston College interviewed a number of former paramilitaries about the Troubles on the understanding transcripts would not be published until after their deaths - but that undertaking was rendered ineffective when the court last year ordered that tapes that contained claims about the killing be given to detectives.
Mr Adams, 65, has always denied IRA membership or any role in Mrs McConville's death and said in March he would be available to meet with detectives if they wished to speak with him.
He stepped down as MP and is a representative for Co Louth in the Irish Dail. The veteran republican presented himself at Antrim police station by prior arrangement with officers.
He issued a statement minutes after the PSNI announced an arrest had been made.
"While I have concerns about the timing, I am voluntarily meeting with the PSNI this evening," he said last night, questioning why police chose to interview him in the run up to an election.
"As a republican leader I have never shirked my responsibility to build the peace. This includes dealing with the difficult issue of victims and their families. Insofar as it is possible I have worked to bring closure to victims and their families who have contacted me. Even though they may not agree, this includes the family of Jean McConville.
"I believe that the killing of Jean McConville and the secret burial of her body was wrong and a grievous injustice to her and her family.
"Well publicised, malicious allegations have been made against me. I reject these.
"While I have never disassociated myself from the IRA and I never will, I am innocent of any part in the abduction, killing or burial of Mrs McConville."
Ms McDonald said he was right to confront this issue.
"There has been a concerted and malicious effort to link Gerry Adams to this case for some considerable time.
"He has consistently and forthrightly rejected any suggestion that he had any part in what happened to Jean McConville 42 years ago or that he has any information about these dreadful events.
"I believe the timing of this latest decision by the PSNI is politically motivated and designed to damage Gerry Adams and Sinn Fein."
She said the party believes dealing with the past is best addressed through an "independent, international, truth recovery process" and supports the latest talks led by US diplomat Dr Richard Haass.
A PSNI spokesman said last night: "Detectives from the serious crime branch investigating the abduction and murder of Jean McConville in 1972 have arrested a 65-year-old man in Antrim. The suspect is currently being interviewed by detectives at the serious crime suite in Antrim police station."
Mrs McConville, a 37-year-old widow, was dragged away from her children in her home in the Divis flats, west Belfast, by an IRA gang of up to 12 men and women after being accused of passing information to the British army in the city.
She was murdered and secretly buried, becoming one of the so-called Disappeared victims of the Troubles.
An investigation later carried out by the Northern Ireland Police Ombudsman rejected the claims that she was an informer.
She was shot in the back of the head and buried 50 miles from her home. Clearly embarrassed by the killing, the IRA did not officially admit responsibility for the murder until 1999 when information was passed to police in the Irish Republic.
It was not until August 2003 that her remains were found on Shelling Hill beach, Co Louth.
Mr McConville, who was in the room when his mother was snatched, told BBC Radio 4's Today programme he knew who was involved but had been beaten and threatened not to say anything about the incident.
"I never told anyone who it was, I still haven't told anyone who it is," he said.
"I do know the names of the people ... I have never told anyone."
He added: "I wouldn't tell the police. If I told the police now, a thing, me or one of my family members or one of my children would get shot by these people.
"Everybody thinks this has all gone away, it hasn't gone away."
Mr McConville said he had seen the people involved on the streets "on many occasions" and "when I see them my blood boils in my body, I just can't stand these people for what they have done to us".
Asked about claims that Mr Adams's arrest was politically motivated, David Cameron's official spokesman told a regular Westminster media briefing: "This is entirely - and rightly so - an independent police matter.
"The fact that there has been an ongoing investigation into this for a period of time is a well-known matter of public record."
The spokesman declined to say whether Downing Street had been given advance notice of the arrest by police.