The duo, aged around 70 years, were staying as tenants in their first floor room, police said, adding the building structure was old and not properly maintained.
"The incident took place in Shahpur locality. Two persons living in the residential building were killed after the roof of their room fell," an official said.
The deceased were identified as Dayaram Hasmukhbhai and his wife Shantaben Dayaram.
The fire brigade and police carried out the rescue operation after the mishap.
Apart from the two casualties, no injuries were reported.