Russian-born Ben Tzion, 31, has been posting photos of himself visiting Iran, Lebanon, Saudi Arabia and Jordan.
His Facebook page includes photos of him inside Medina Prophet’s Mosque, one of Islam’s holiest sites.
“People of Saudi Arabia would stand with the Jewish nation side by side,” he said in a Facebook post with a photo of him performing the Saudi sword dance in a traditional ankle-length garment known as a “thobe”.
“Peace in the Middle East with respect and love towards each other,” he said in another post.
Non-Muslims are prohibited from visiting Mecca and advised not to enter parts of central Medina, where the mosque is located. But Mr Tzion said religious sites in Medina were open to the public.
Speaking to the Times of Israel, Mr Tzion – who became an Israeli citizen in 2014 – said visiting Muslim countries was “a hobby”, describing his message as “respect for other cultures and faiths”.
“No-one in the Arab world ever approached me with hostility,” he said.
“They tell me they love Israel and the Jewish people.”
He said he had acquired visas and entered all the holy sites legally, though not specifying which of his passports he travelled on.
Mr Tzion has also posted photos of his visits to the Iranian cities of Tehran and Qom. Israel and Iran are arch foes and citizens of the Jewish state are not allowed to visit Iran.
Despite his expressions of peace, Mr Tzion’s post was met with outrage.
The Arabic hashtag “A Zionist at the Prophet’s Mosque” has attracted more than 90,000 tweets in the past 24 hours.
“The scholars are in prisons and the Zionists are at the Prophet’s Mosque. It is a sad thing,” said one Twitter user in Arabic.
“In the era of Al Saud [the Saudi royal family], the occupying Zionists, the enemies of Islam and Muslims… defile the mosque of the seal of the Prophet,” said another.
Another user tweeted: “The current hashtag: A Zionist at the Prophet’s Mosque; the next hashtag: A Zionist on the pulpit of the Prophet’s Mosque; and the following hashtag: A Zionist is the imam of the Mecca Mosque.”
According to the Times of Israel, the huge number of angry comments on Instagram led to the photo-sharing platform’s decision to suspend Mr Tzion’s account.
The images come at a time when relations between Israel and Saudi Arabia are seen to be improving over their shared opposition to Tehran’s growing influence in the region.
The Israeli army’s chief of staff, Maj Gen Gadi Eizenkot, recently told an online Saudi newspaper that Israel was prepared to share “intelligence information” with Riyadh.