Turei reiterated calls for Israel to lift its "inhumane" blockade and "help the people of Gaza to rebuild their homes and lives".
"Marama's trip was focused on drawing attention to the dire humanitarian situation in Gaza, where Palestinians are struggling to survive," she said.
A Ministry of Foreign Affairs (MFAT) spokesman said the New Zealand Embassy in Ankara, Turkey, had spoken to Davidson, and was in touch with her family.
"We understand Ms Davidson agreed to leave Israel voluntarily and arrangements are in progress."
The ship she was travelling on, the Zaytouna-Olivia, was intercepted by the Israeli Navy about 35 miles off the coast of Gaza yesterday.
The Israeli Defence Force said the takeover occurred "without incident" and followed attempts by Israeli authorities to stop the boat through diplomatic channels.
The IDF said the blockade of Gaza was lawful and that the trip by the protest ship was an intentional attempt to breach it.
Most of the women were detained in Giv'on Prison on the outskirts of Tel Aviv.
Davidson's mobile phone was confiscated by authorities and she could not be reached.
In a video on the Kia Ora Gaza website which was pre-recorded in case the flotilla was detained, Davidson said there was no reason to detain the women.
"We are peaceful women who started by principles of peace. The Israeli oppression forces had no reason to kidnap us, to take us hostage. They could have just let us through to Gaza."
The MP set off in September to join the Womens' Boat to Gaza which was sponsored by the Freedom Flotilla Coalition, pro-Palestinian groups mainly in Europe.
Others on board include Northern Ireland's Mairead Maguire, the 1976 Nobel Peace laureate, retired US Army Colonel Ann Wright and Fauziah Hasan, a Malaysian doctor.
It was captained by Australia's Madeline Habib.
Prime Minister John Key was critical of Davidson yesterday, saying her protest was a "less than perfect look".
