Palestinian Prime Minister Ismail Haniya has appealed to the international community for help to secure the release of his deputy.
Nasser al-Shaer was detained by the Israeli army early on Saturday.
The Israeli army said it had detained Mr Shaer because he was a member of a "terrorist organisation".
Israeli troops shot dead a Palestinian and wounded three near Nablus in the north of the West Bank on Sunday, Israeli and Palestinian sources said.
Mr Haniya, from the Islamic militant movement Hamas, said the arrest was part of an Israeli attempt to undermine the Palestinian political system
Mr Shaer is also a member of Hamas which formed the Palestinian government after winning parliamentary elections earlier this year.
He was seized in a raid on his home in the West Bank town of Ramallah.
Israeli crackdown
Four other ministers and many senior officials are also being held by Israel following the capture of an Israeli soldier by militants in Gaza in June. It has released several others.
Mr Shaer's wife said her husband had been in hiding since Israel began its crackdown in late June.
He was rarely home during that period, she said.
An unnamed Israeli army spokesman quoted by the AFP news agency said Mr al-Shaer's detention was "part of our fight against the radical Hamas movement".
Israel's crackdown has largely focused on the Gaza Strip, Hamas's stronghold.
But politicians from the Islamist movement - which does not recognise Israel - have also been detained in the West Bank.
Israel's position is that Hamas is a terrorist organisation and its leaders are therefore "targets for arrest".
In a separate development, an Israeli soldier was shot dead by a Palestinian gunman in the West Bank, the army said.
The gunman was then shot dead, officials say. The incident happened at a checkpoint near the city of Nablus.
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