The Libya counter-terrorism force detained the father, Ramadan Abedi, outside his home in the Tripoli suburb of Ayn Zara on Wednesday afternoon.
A witness said he was handcuffed by armed men who drove him away in two unmarked vehicles.
The force, known as Rada, detained the brother Hashem Abedi, who was born in 1997, on Tuesday evening on suspicion of links to Islamic State, spokesman Ahmed Bin Salem said. He did not give any details on the reasons why the father was arrested.
But Hashem Abedi had been in touch with Manchester Arena attacker Salman Abedi, Bin Salem said, and was suspected of planning to carry out an attack in the Libyan capital.
“We have evidence that he is involved in Daesh (Islamic State) with his brother. We have been following him for more than one month and a half,” Bin Salem said. “He was in contact with his brother and he knew about the attack.”
He said the younger brother had travelled from London to Tripoli on April 16.
Salman Abedi, 22, was born in Britain to Libyan parents. Britain’s interior minister said earlier that he had recently
returned from Libya and had likely not acted alone. His father lives in Tripoli.
Meanwhile, US entertainer Ariana Grande has suspended her Dangerous Woman tour following the attack on her Manchester show, which killed 22 people.
A spokesman for the 23-year-old announced the decision on Wednesday evening following widespread speculation that dates would be affected.
Grande’s next engagements were two nights at the O2 Arena in London on Thursday and Friday before heading to mainland Europe.
There has been no word on the six-date tour of Australia and New Zealand scheduled for September.
“We are deeply saddened by this senseless tragedy and our hearts and thoughts are with those impacted by this devastating incident,” promoters Live Nation said in a statement.