Mohammed Abu Tir was taken to custody on suspicion of being "involved in terrorist activities", an army spokeswoman told AFP.
He was arrested in an overnight raid in Kafr Aqeb area near to Ramallah in the occupied West Bank, she added. Abu Tir is a Hamas member of the Palestinian Legislative Council from east Jerusalem.
He was previously held by Israel for a year without charge, eventually being released in 2012. Six other members of the 132 member Palestinian Legislative Council are currently detained by Israel, according to the Palestinian human rights organisation Addameer.
According to Addameer, three of them are Hamas members, one is from Fatah and two others from the leftist Popular Front for the Liberation of Palestine (PFLP), which Israel considers to be a "terrorist organisation".
The Hamas-dominated parliament has not met since the Islamist movement took over the Gaza Strip in June 2007, ousting Fatah forces loyal to Palestinian president Mahmud Abbas.