Mr Adams, who has vehemently rejected the allegations made by former republican colleagues that he had a role in ordering the notorious IRA killing in 1972, voluntarily presented himself for interview at a police station in Antrim.
No one has ever been charged with the murder.
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 last month with aiding and abetting the murder.
In the wake of the recent developments in the case, Mr Adams, who has always denied membership of the IRA, last month said he would be available to meet with detectives if they wished to speak with him.
Mr Adams, 65, a former MP for West Belfast and now a representative for Co Louth in the Irish Dail, presented himself at Antrim police station by prior arrangement with officers.
He issued a statement minutes after the Police Service of Northern Ireland (PSNI) announced an arrest had been made.
“Last month I said that I was available to meet the PSNI about the Jean McConville case,” he said.
“While I have concerns about the timing, I am voluntarily meeting with the PSNI this evening.
“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.”
A PSNI spokesman said: “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 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.