A police spokesman confirmed the arrest of Amro Abu Khdair but said it was not connected to Friday's funeral.
He declined to give the reason for the man's arrest.
Images of baton-wielding Israeli officers beating the pallbearers, who at one point nearly dropped Al Jazeera journalist Abu Akleh's coffin, drew widespread international condemnation and added to anger over the killing of the reporter during an Israeli military raid in the city of Jenin in the West Bank on May 11.
Mr Abu Khdair's lawyer, Khaldoon Nijm, said his client was arrested on Monday but that the charges were not revealed to him and were based on information from Israel's domestic security service.
He said Mr Abu Khdair later told him he was questioned about the funeral.
A police official said any connection made to the funeral would amount to a “cheap conspiracy”.
Mr Abu Khdair's custody had been extended until Sunday, police and Mr Nijm said.
A second pallbearer, who asked not to be identified, told Reuters he had been questioned by police though not arrested.
Israel's Internal Security Minister Omer Barlev said on Saturday he and the police commissioner had appointed a panel to carry out a “comprehensive investigation of what happened during the funeral, in order to learn lessons from the event”.
Separately, Israel is conducting a probe into Abu Akleh's death. The Palestinian authorities are also investigating her killing.
The Palestinians accuse Israeli forces of assassinating her. Israel has denied targeting the correspondent, saying she may have been shot accidentally by a soldier or a Palestinian gunman as they exchanged fire in Jenin.