The arrest took place on Tuesday evening while Aljazeera was airing a recorded interview with Isam al-Barqawi, better known as Shaikh Abu Muhammad al-Maqdisi.
In the interview, al-Barqawi told Aljazeera's correspondent in Amman: "I have reservations on expanding jihadi operations or what others call suicide or istishhadiya (martyrdom)." He was referring to attacks on civilians rather than military targets.
"I see that expansion is only needed when it is essential," he added.
Islamist and security sources have said the 43-year-old Muslim cleric - who moulded the views of al-Zarqawi - was released only on 28 June after a six-month detention at intelligence headquarters following his acquittal at a trial of Jordanian and Saudi sympathisers of al-Qaida.
He had been under close surveillance by the authorities at his house near Zarqa, east of the capital, where fellow Jordanian al-Zarqawi was born.
Jordanian officials could not be immediately reached for comment.
Al-Barqawi is said to have taught al-Zarqawi Islamic ideology while they shared a cell-block for four years between 1995 and 1999.
Both were freed in an amnesty, and al-Zarqawi later went to Afghanistan, then to Iraq, where his followers have waged a campaign of car bombings, attacks and kidnappings.
Al-Barqawi was put on trial again last year among a group accused of conspiring to commit attacks against US targets in Jordan.
He was acquitted but remained in prison until his release last week.
From his cell in Jordan, al-Barqawi wrote to al-Zarqawi in a message posted on the internet in October asking al-Qaida's suspected point man in Iraq to "spare the blood of fighters and Muslim money" until a more appropriate time to wage an all-out war.