A Police Service of Northern Ireland [PSNI] statement said: "A 65-year-old man has been arrested this evening in connection with the abduction and murder of Jean McConville."
Mr Adams denied he had been arrested and said he had pre-arranged to meet police voluntarily.
He has vehemently rejected the allegations made by former republican colleagues that he had a role in ordering the notorious IRA killing in 1972.
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, last month Mr Adams, who has always denied membership of the IRA, said he would be available to meet with detectives if they wished to speak with him.
Tonight the Sinn Fein president confirmed he had met detectives, but said it was on a voluntary basis.
"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."
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.
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. The IRA did not admit her murder until 1999 when information was passed to police in the Irish Republic.
She became one of the so-called Disappeared, and it was not until August 2003 that her remains were found on Shelling Hill beach, Co Louth.