Malouh, who was arrested in 2003 and is about 60-years old, is said to be ill.
A member of the Palestine Liberation Organisation's executive committee, he is considered close to Abbas and could serve as a mediator with Hamas.
Abbas has refused to talk to Hamas since its forces took over the Gaza Strip in the middle of June, leaving Abbas in control of the West Bank.
On Tuesday, Khaled Meshaal, Hamas' exiled leader, told Al Jazeera that the new Palestinian caretaker government appointed by Abbas was "illegitimate and illegal".
However, Meshaal said that he "supported dialogue" with the president.
David Baker, an official in the office of Ehud Olmert, the Israeli prime minister, said the cabinet committee approved the list by a vote of 7-2.
Avi Dichter, Israel's public security minister and a former head of the Shin Bet internal security service, supported the release.
After touring a prison in Israel's southern Negev Desert, where some of the Palestinian prisoners are being held, he said: "This is certainly an acceptable risk Israel is taking in order to strengthen the regime of Abu Mazen [Mahmoud Abbas]."
Saeb Erekat, a Palestinian negotiator, said he welcomed the freedom of any Palestinian prisoners, but urged Israel to free more of them.
Israel holds about 10,500 Palestinian prisoners.
Criticism came from Ashraf al-Ajrami, the Palestinian minister for prisoner affairs.
He said: "Israel insists on releasing those who have limited sentences. We want a release of prisoners who received long sentences."
In a separate development, Israel freed Nasser al-Shaer of Hamas, the education minister in the cabinet dismissed by Abbas after the Gaza takeover.
Shaer was arrested in May and held in administrative detention.
The Israeli army said he has promised to sign a public declaration renouncing his Hamas membership and stating he would not take any position in the Palestinian Authority for Hamas or "any other illegal organisation".