Dozens of people gathered early on Monday at the Beit Hanoun crossing in north-eastern Gaza to block access to the organisation - which calls itself "This is Bahrain" - local media reported.
The first public visit by a Bahraini delegation to Israel has sparked angry reactions, coming days after US President Donald Trump's decision to recognise Jerusalem as Israel's capital.
The deputy chairman of Hamas' political wing took to Twitter on Monday to strongly condemn the group's attempt to visit the besieged Palestinian enclave.
"As they were prevented from entering al-Aqsa mosque, they will not be allowed to enter Gaza," Mousa Abu Marzouk said
"These people do not represent Bahrain, which has helped us in all our battles," Abu Marzouk added.
The Palestinian National and Islamic Forces issued a statement, labelling the delegation as "shameless".
"There is no place for people seeking to normalise relations with Israel in Gaza or in any other part of Palestine," the party said.
Speaking to Israeli media on Saturday, Sheikh Fadil al-Jamri, a member of the delegation, said they had been sent by Bahrain's King Hamad bin Isa al-Khalifa with a "message of peace".
The controversial trip comes amid speculation that Bahrain could become the first Gulf states to normalise relations with Israel.
In September, King Hamad reportedly said he has grown "tired" of Arab states' boycott of Israel and called for diplomatic ties to be established between the two countries.
He also told a leading US-based rabbi that Bahraini citizens were free to visit Israel.
In response to growing criticism of the visit, "This is Bahrain" issued a statement
on Sunday night - cited by Manama's official BNA
news agency - insisting the visit was unofficial.
"The delegation, which includes some foreign nationals from different religions residing in the Kingdom of Bahrain, does not represent any official body in the kingdom," it said.
"The delegation represents solely the society and has undertaken the visit on its own initiative."
The 24-member group, which is on a four-day tour, includes Sunni and Shia Muslim leaders, Christians, the leader of a Hindu temple, and a Sikh.
Bahrainis have expressed anger online over the visit and voiced their support for Palestinians.
Israel has long faced resistance to its efforts to improve ties with Arab nations in the region because of its 50-year occupation of Palestinian territory.
It has, however, recently seen increased behind-the-scenes cooperation with some Arab countries, particularly in their opposition to Iran.