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Boston College interviewed a number of former paramilitaries about the Troubles on the understanding transcripts would not be published until after their deaths - but that undertaking was rendered ineffective when the court last year ordered that tapes that contained claims about the killing be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.