A section of Anna Salai - a major road in the eastern city of Chennai - collapsed, swallowing the bus and a car in front of the Church Park Convent.
It is understood the convent, which was established in 1909, did not suffer damage in the incident.
It has emerged construction on a new underground railway line caused the road surface to give way at around 2pm on Sunday.
An official from Chennai Metro Rail Limited (CMRL) was quoted by The Hindu as saying: "We were carrying out a process called cutter-head intervention as part of tunnelling work.
"As the soil strata was loose, the road caved in. We will carry out restoration work immediately."
Emergency service crews sealed off the area and a crane was used to winch the vehicles out of the hole.
CMRL insisted a check on the tunnel currently under construction was made "just before the incident but no damage to the road was found".