Huda, the wife of Nasser al-Shaer, said on Saturday that Israeli troops burst into her home at around 4:30am local time and took her husband away.
She said her husband had been in hiding since Israel began its crackdown in late June after fighters in the Gaza Strip infiltrated southern Israel and captured an Israeli soldier.
She said he had rarely been home during that period.
An Israeli army spokesman confirmed that troops had taken al-Shaer into custody, saying it was "due to his membership of a terrorist organisation".
Saeb Erekat, the most senior Palestinian negotiator, condemned the arrest and said "this complicates" a recent attempt by Mahmoud Abbas, the Palestinian president, to forge a unity government, to ease a Western aid embargo against the Hamas administration.
With al-Shaer's arrest, four members of the Hamas-dominated Palestinian cabinet and about 28 Hamas members of parliament are in Israeli custody. Four other ministers have been detained and released.
Despite the arrests of Hamas officials, and a seven-week offensive in Gaza, the Israeli soldier, Corporal Gilad Shalit, remains in captivity.
Also on Saturday, the Egypt-Gaza border terminal reopened, giving hundreds of stranded Palestinians the chance to return to the Gaza Strip for the first time in a month.
Captain Amr Osama, Egypt's tourism police, said the crossing will be open for two days in both directions.
Wail al-Dahduh, Aljazeera’s correspondent in Gaza, reports that a spokesperson for the European monitors at the Rafah crossing confirmed that the crossing will be opened for at least two days.
Hundreds of Palestinians lined up
to return to the Gaza Strip
Several hundred Palestinians gathered in front of the crossing early on Saturday waiting to return to the Gaza Strip.
About 130 Palestinian deportees also were taken by bus from Egypt to Gaza.
Al-Dahduh said at least 10 buses with Palestinian passengers holding residencies in other Arab countries crossed over. The Palestinians were seeking to leave Gaza, the correspondent said.
Hundreds of state security troops were deployed in front of the gates to prevent any skirmishes among the travellers and the crossing officials.
Inside Gaza, buses that can usually carry 50 people were crammed with more than twice that number to get people across the border as quickly as possible, said a security official who spoke on condition of anonymity because he was not authorised to speak to the media.
Eleven Palestinians who recently were hit with shrapnel in the Gaza Strip crossed into Egypt and were taken by ambulance to a hospital in al-Arish to undergo surgery, said hospital official Ahmed Saleh.
The Rafah crossing opened about a week ago for one day but only for people travelling from Gaza to Egypt.
The last time Palestinians could cross from Egypt to Gaza was in mid-July.
Saturday's opening was the third time the crossing has opened since the latest fighting erupted in Gaza on June 25.