She said they would go to frontline medical workers.
An Israeli defence official confirmed that the vaccines were on their way to Gaza after approval, saying it was "not in Israel's interest to have a Gaza health crisis".
Israeli politicians had debated whether to allow the delivery of vaccines into Gaza, which has been under an Israeli-Egyptian blockade since Hamas, a militant group, seized power from rival Palestinian forces in 2007.
The Palestinian Authority administers parts of the West Bank and co-ordinates with Israel on security and other matters.
Some legislators said the delivery should be linked to progress on the release of two Israeli captives held by Hamas and the remains of two Israeli soldiers killed in 2014.
They also expressed concern that the first batch of vaccines would go to Hamas members rather than medical personnel.
Gaza is home to more than two million Palestinians, many of whom live in close confines, and has yet to receive any vaccines.
Authorities have reported more than 53,000 cases and at least 538 deaths since the start of the pandemic.
Israel launched one of the world’s most successful vaccination programmes, inoculating more than a third of its population of 9.3 million since December.
Rights groups say it has an obligation as an occupying power to share its vaccines with the Palestinians. Israel denies such an obligation and says its priority is its own citizens.
