The attacks that Udda was allegedly involved in included one at a bus stop near the Tsrifin army base southeast of Tel Aviv, which killed seven soldiers and wounded 14 in 2003.
Another attack the same year targeted a cafe in Jerusalem’s German Colony neighbourhood, killing six and wounding 40.
Fawzi Barhum, a Hamas spokesman, said the arrest was "the fruit of dangerous security co-ordination between the Palestinian Authority and the [Israeli] occupation, because he was wanted and hunted by both parties".
"The continuation of this security co-ordination is going to bury reconciliation alive because it comes in the context of uprooting Hamas and strengthening Fatah [rival Palestinian group]," he told AFP.
Born in 1963, Udda is a father of four. He formed a Hamas cell in his village Ein Yabrud, northeast of Ramallah, in early 1990s.
Long-running tensions between Hamas and Palestinian president Mahmoud Abbas's Fatah party boiled over when Hamas fighters drove his forces from Gaza in June 2007, seizing power in the coastal enclave.
Since then each movement has accused the other of persecuting its rivals within the territory under its control.