Khaled Abu Arafeh was released from a police station inthe Jewish settlement of Maale Adumim more than five hours after he was detained.
Abu Arafeh was taken into custody at a checkpoint at the entrance to al-Azaria, a suburb of east Jerusalem which is technically part of the occupied West Bank. Israel has banned Abu Arafeh from entering the West Bank.
Hamas said Israeli police had accused him of "illegally entering an area under Palestinian control".
Witnesses said police had manhandled Abu Arafeh out of the car he was travelling in with two other people before bundling him into a jeep. His bodyguard was also briefly detained and later released.
The 45-year-old minister is one of the main Hamas officials in the Jerusalem area where he lives. He has been arrested by Israel several times in the past.
Israel has vowed to have no dealings with Hamas unless the group, responsible for scores of suicide bombings in Israel over the 10 years, abides by previous agreements, renounces violence and recognises its right to exist.
Israel bans all political activity in east Jerusalem, which it occupied in the 1967 Middle East War and subsequently annexed.
Air attack
Just hours later Israeli warplanes have bombed and wrecked two offices of an armed wing of Palestinian President Mahmoud Abbas's Fatah movement in Gaza City.
Helicopters fired missiles at two headquarters of the al-Aqsa Martyrs Brigades in Gaza City, but Palestinian officials said there were no casualties.
An Israeli army spokeswoman said both strikes had targeted offices of the Al-Aqsa Martrys Brigades, an armed wing of Fatah Israel blamed for firing rockets at its towns and cities on Thursday.
One of the rockets fired from Gaza struck an Israeli factory near the town of Ashkelon and set it ablaze, injuring one Israeli. Another struck inside the town of Sderot but caused no injuries.
Austerity measures
Meanwhile the Hamas-led Palestinian government has called for emergency aid to pay last month's salaries and has introduced austerity measures to slash public spending.
"We are hoping to receive emergency aid to overcome the Palestinian Authority's budget deficit and to pay the salaries of its civil servants," said finance minister Omar Abdelrazek, himself a Hamas member.
He said the Palestinian Authority employs around 140,000 civil servants and security service personnel, together accounting for a monthly salary cheque of A$162.55 million.
"We are expecting aid from Arab and Islamic countries, and friends. We have had promises of aid worth nearly $US80 million ($A110.2 million) and I hope they will reach us quickly because we don't have money to pay the salaries," he said.
As part of a series of sanctions imposed in the aftermath of Hamas's election win, Israel has since February stopped transferring customs duties it previously collected for the Palestinian Authority.
Mr Abdelrazek said his ministry was working on a package of austerity measures in a bid to slash public spending and shoring up efforts to secure alternative sources of foreign funds.
US aid increase
Bankrupt and boycotted by the West, the Palestinian Authority has already been in the grip of financial crisis for months and is heavily dependent on foreign aid receipts.
Mr Abdelrazek said that the Palestinian treasury has run up bank debts totalling A$881.6 million and owes another A$860.94 million to other institutions.
Meanwhile the United States is looking to boost humanitarian assistance to the Palestinian people while refusing to provide aid
to the Hamas-led government.
US State Department spokesman Sean McCormack said Washington was preparing to announce in the coming days the results of its review of aid prompted by the emergence of the Palestnians' new militant leadership.
The United States has vowed to maintain humanitarian aid for the Palestinians and is considering an increase in the funds available through the UN Relief and Works Agency (UNRWA).