The center was one of 10 sites attacked beginning Wednesday.
The couple's toddler son, Moshe Holtzberg, was taken out of the center by an employee, and is now with his grandparents.
"Gabi and Rivky Holtzberg made the ultimate sacrifice," said Rabbi Moshe Kotlarsky, vice chairman of the educational arm of Chabad-Lubavitch.
The Holtzbergs arrived in Mumbai in 2003 to serve the local Jewish community. The two ran a synagogue, offering religious instruction and helping people dealing with drug addiction and poverty, Kotlarsky said.
Gavriel Holtzberg, 29, was born in Israel and moved to the Crown Heights section of Brooklyn with his parents when he was nine. His 28-yera-old wife was also Israeli-born.
Twelve hours after gunmen stormed the center Wednesday, Sandra Samuel, a cook at the center, heard little Moshe's cries outside the room in which she had barricaded herself. She opened the door, grabbed the toddler and ran outside with another center worker.
The little boy's pants were soaked with blood, and Samuel said she saw four people lying on the floor as she fled.