The website went live on Sunday, Ahmad Dawa told AFP, and is intended to expand the state news service's audience.
"We want to address all those who speak this language," he said.
"Our objective is to reach the largest number of people possible and to clarify Syria's image," following more than three years of deadly conflict in the country, he added.
Dawa said the agency hoped to reach residents of the Israeli-occupied Golan Heights, Arab residents of Israel and Israelis "in a way that reflects the truth".
"We want to diffuse impartial information... on the attacks and violations committed against the Palestinian and Syrian people."
In tandem with the new Hebrew site, SANA also launched a page in Farsi, the language of its key ally Iran.
Dawa said it was the first time the agency's news had been made available in either language and that the Hebrew and Farsi departments each employed six people.
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SANA already has seven language services: Arabic, English, French, Spanish, Turkish, Russian and Chinese, while state television also offers a daily news bulletin in several languages.
The site is often dominated by news about President Bashar al-Assad, and stories proclaiming the government's advances in what it terms a battle against "terrorists".
In 2002, state television briefly experimented with Hebrew bulletins but ended them because of a shortage of Hebrew speakers in the country, where the language is not taught at universities.
Mohamed Khodr Omar, a member of SANA's new Hebrew department, told AFP that he and most of his colleagues had learned the language in the army under a programme in operation from 1978 to 1990.
Syria and Israel are officially at war and the Jewish state has occupied a large portion of the Golan Heights plateau since 1967.
It has annexed the area, but the move was never recognised by the international community.
In May 2012, just 22 Jews remained in Syria of the 30,000 who were living in the country in 1948 when Israel was established.