Khaled Abu Arafa, minister of Jerusalem affairs, was detained on Thursday as he was travelling to Izzariya, a suburb near Jerusalem, where he was planning to open an office.
The Israeli army said Abu Arafa was detained because he is barred from the area.
An army spokesman said: "The Hamas minister was detained at about 9am (0600 GMT). He was not questioned at any point and was released at 2pm."
Security officials quoted by the Haaretz website said Abu Arafa was detained because as the holder of an Israeli identity card he is banned by Israel from entering areas administered by the Palestinian Authority.
Hamas officials earlier said that Israeli vehicles with paramilitary policemen inside appeared to have been waiting for him.
Walid al-Umari, an Al Jazeera reporter in Ramallah, quoted one of Afara's bodyguards as saying that the Palestinian minister was intercepted at an Israeli checkpoint and was taken to an Israeli army office in Jerusalem.
He was released five hours later after being taken to an Israeli police station in the Jewish settlement of Maale Adumim outside Jerusalem.
Ghazi Hamad, the Palestinian cabinet spokesman, said Israel was undermining the work of the new government.
"The arrest of a cabinet minister proves the falseness of Israel's arguments that it seeks peace," Hamad said.
It appears that Abu Arafa was arrested for trying to open the office. Part of Izzariya is in Jerusalem, which is at the centre of the Israeli-Palestinian conflict.
Israel claims the entire city as its capital, while the Palestinians claim the eastern half for the capital of a future state.
Abu Arafa, a Jerusalem resident born in 1961, has been detained several times by Israel in the past.