Jean McConville's daughter, Helen McKendry, told CNN that the arrest was a welcome step in the family's long struggle to find justice.
"There's been silence over my mother's murder for 22 years and then I went public, and then we got her body back in 2003 and gave her a proper burial. Now we have learned Gerry Adams has been arrested in connection with the murder," McKendry said.
"I can only do like everyone else in my case and hope that he will be brought to a court of law and be charged with my mother's murder, so my family can get truth and justice for my mother."
Adams has long denied having any role in the death of McConville, a widowed mother of 10 who was reportedly killed by the IRA because the group believed she was a spy for the British army.
The Sinn Fein leader continued to be questioned Thursday, a day after he surrendered himself to police, his party said.
Martin McGuinness, a Sinn Fein member and the Deputy First Minister of Northern Ireland, told reporters in Belfast that the arrest was unnecessary, unjustified and politically motivated.
He said he had seen the "dark side" of Northern Ireland policing "flex its muscles in the course of the past couple of days" and that the arrest was a "'deliberate attempt to influence the elections that are due to take place in three weeks' time."
McGuinness said he was confident that Adams would be able to rejoin election campaigning shortly and would "continue to lead our party in a very positive way."
'Take away the fear'
McKendry said she hoped that the progress made in the peace process in recent years would make it more likely that charges could be brought over her mother's death.
"I do think that there would be people willing to come forward when they take away the fear, and will come forward to help," she said.
"A lot of the members of the IRA have approached myself and my husband and spoke about what happened and a lot of them did not agree with what happened. A lot of them wanted to see Gerry Adams stand trial for this."
Earlier, her brother, Michael McConville, echoed her words.
"The McConville family is glad to see police are taking our mother's murder seriously and are doing all they can to bring the people that murdered her to justice," he said.
"An awful lot of people in the north and south of Ireland are glad to see Gerry Adams being arrested for this."
Adams: I am innocent of abduction, killing
In a statement released shortly before the Sinn Fein leader surrendered himself for questioning Wednesday, Adams, 65, vehemently denied any involvement in the killing.
"I believe that the killing of Jean McConville and the secret burial of her body was wrong and a grievous injustice," Adams said in the statement posted on his party website. "Malicious allegations have been made against me. I reject these."
The questioning of Adams was not unexpected. Adams said he told authorities last month that he was willing to meet with investigators.
"While I have never disassociated myself from the IRA and I never will, I am innocent in the abduction, killing or burial of Mrs. McConville," Adams said.
Long associated with the IRA, once considered the armed wing of Sinn Fein, Adams is a prominent Catholic politician who helped broker peace in Northern Ireland. Today, Sinn Fein is Ireland's second-largest opposition party.
The Police Service of Northern Ireland said a 65-year-old man, whom it declined to identify but described as a suspect in the McConville case, remained in custody Thursday.
Single gunshot wound
Northern Ireland is part of the United Kingdom, and Protestant loyalists wanted to keep it that way. Catholics were fighting to force the British out and reunite the north with the rest of Ireland.
Known as the Troubles, the conflict lasted 30 years, ending in 1998 with the Good Friday Agreement that brokered peace. The agreement provided a political framework for power-sharing among the parties.
The IRA admitted in 1999 to killing a number of people who have become known as "The Disappeared" -- those who vanished during the Troubles.
Among the victims was McConville, whose remains were found partially buried on a beach in County Louth in 2003. She died of a single gunshot wound to the back of the head.
McConville, 38, was taken from her home in Belfast in December 1972, McKendry told CNN in a 2012 interview.
"They came about tea time and they dragged her out of the bathroom and dragged her out," said McKendry, who was a teenager at the time. "All I ever wanted was to know the reason why they killed my mother."
The investigation into McConville's killing was revived by authorities after the release, following a protracted legal battle, of certain interviews given by members of the IRA, who implicated Adams.
The recordings were made by Boston College as part of the Belfast Project, which is a collection of interviews conducted with former Northern Irish paramilitary fighters. They provide an oral history of the decades of fighting.
Participants in the project were told their recorded interviews would be kept secret until their deaths. Last year a U.S. court ruled that tapes of deceased interviewees that contained claims about the killing be given by Boston College to police in Northern Ireland.
One of those featured in the tapes was Brendan Hughes, a now-deceased former commander of the Irish Republican Army.
Peter Taggart reported from Belfast, Laura Smith-Spark wrote and reported from London and Chelsea J. Carter reported and wrote from Atlanta. CNN's Greg Botelho and Nic Robertson contributed to this report.