KOLKATA — On bustling Brabourne Road in central Kolkata, vendors line sidewalks packed with pedestrians, while cars, motorbikes and rickshaw pullers fill the street. Amid the urban din, the Magen David Synagogue sits silent and empty. A Muslim guard stands watch outside. With an estimated 25 Jews remaining in this city of 14 million people, the synagogue is rarely used.

Magen David and the city’s two other synagogues used to be packed on Jewish holidays. For the first half of the 20th century, Kolkata, then known as Calcutta, was home to nearly 3,500 Jews. At its peak during World War II, the population grew to about 5,000 when Jews from Burma and Europe moved to the city seeking refuge, according to Jael Silliman, one of Kolkata’s remaining Jews and the author of a recent novel on the community.

“We thrived here,” said Ms. Silliman, 58. “We had Jewish schools and our own newspapers. But now it’s mostly memories. In a few years we’ll all be gone.”...