The deadly explosion occurred Monday night outside the arena where the concert had just wrapped up about 10:30 p.m. local time, the Greater Manchester Police said.
The man was arrested in south Manchester Tuesday, the day after the explosion that killed at least 22 people and injured more than 50. Twelve children under the age of 16 were among those injured.
The attacker died at the arena, police said.
The Islamic State group says one of its members planted bombs in the middle of crowds in Manchester, though police have spoken only of "an improvised device" used in the attack.
IS says "a soldier of the caliphate planted bombs in the middle of Crusaders gatherings" then detonated them. It did not say whether the attacker was killed.
The group claimed that "30 Crusaders were killed and 70 others were wounded," higher than the totals confirmed by authorities in Manchester.
There was mass panic after the explosion at the end of the concert, which was part of Grande's The Dangerous Woman Tour. The singer was not injured, according to a representative.
The 59 injured people were being treated at eight area hospitals, police said.
"This has been the most horrific incident we have had to face in Greater Manchester and one that we all hoped we would never see," Chief Constable Ian Hopkins said in a prepared statement.
"Terrorists attempt to disrupt our lives and create distrust and fear in communities," he said. "We have a long history in Greater Manchester of communities standing together during difficult times."
People were encouraged to avoid the area in the city center. The train station near the arena, Victoria Station, was evacuated and all trains canceled.
Witnesses reported hearing two loud bangs coming from near the arena's bars and seeing dozens of people on the floor of the arena as they scrambled to flee.
Catherine Macfarlane was on her way out at the end of the concert when she heard what she described as a "massive explosion."
"... You could feel it in your chest. It was chaotic. Everybody was running and screaming and just trying to get out of the area," she told Reuters.
"We saw young girls with blood on them, everyone was screaming and people were running," concertgoer Sasina Akhtar, told the Manchester Evening News.
Jane Pearson went to the concert with her 21-year-old daughter. She said the arena was full of young children, the Telegraph reported.
"I can't imagine what goes in to the heads of these people that want to hurt children? And families who have come together for such a happy occasion," she said. "It's disgusting. It's absolutely disgusting."
British Prime Minister Theresa May said the government is working to learn "the full details of what is being treated by the police as an appalling terrorist attack."
She said her thoughts are with the victims and the families of those who have been affected.
The government is expected to call an emergency cabinet meeting to deal with the incident.
Frantic loved ones of young people missing after an explosion at an Ariana Grande concert have taken to Twitter and Instagram with their photos and pleas for help.
Manchester Arena can accommodate 21,000 people, the arena says on its website.
The Department of Homeland Security says there is no evidence of credible threats against music venues in the U.S. The department says the U.S. public may experience increased security in and around public places and events.
Grand Prairie police confirmed to KXAS-TV (NBC5) that there would be added officers at the Verizon Theater for the John Legend concert Monday night.
DHS said it is closely monitoring the situation at Manchester Arena and working with U.K. officials to obtain additional information about the cause of the explosion.
The government is urging U.S. citizens in Manchester to heed directions from local authorities and be vigilant about their security.
Britain's terrorist threat level has been set at "severe" in recent years indicating an attack is highly likely. Police said the explosion is being judged a terrorist attack unless new information proves otherwise.
In November 2015, a Paris concert hall, the Bataclan, was targeted by terrorist carrying out a series of coordinated attacks that left 130 people dead. Eighty-nine concertgoers were killed and hundreds were injured.
The New York Times and Associated Press contributed to this report.
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