Protestors on Wednesday symbolically sealed the synagogue during a protest against Israel's strikes on Gaza that by Friday had killed 776 Palestinians and injured more than 3,000 people.
'We are asking the city administration to close the synagogue and verify the presence of the Jewish community here,' said Ahmad Suyanto, a member of the Surabaya City Council.
He said Judaism was not one of six religions recognised in Indonesia - Islam, Protestantism, Catholicism, Hinduism, Buddhism and Confucianism.
'We don't know what Jews here look like, whether they look like those in Israel,' he said.
Suyanto said the council was acting on demands made by protestors angered by the deaths of Palestinians.
'However we should act within legal boundaries and not take the law into our own hands,' he said.
The synagogue was built in the 1930s when Indonesia was under Dutch occupation.
It is estimated that there are fewer than 100 Jews in Indonesia, the world's most populous Muslim country where around 85 percent of its 220 million population follow Islam.