Twenty Indian pilgrims were heading to the city of Qom, considered holy in Shia Islam, on Sunday night when the accident happened.
"I have got the report from Indian Embassy in Tehran. A bus carrying 20 Indian pilgrims on way to Qom met with an accident last night. Unfortunately, we lost Ms. Kulsum Fatima aged 14 years because of head injuries," Ms Swaraj tweeted.
Another national named Mohammad Ali is in the ICU, while 18 Indians were discharged after first aid, she said.
Qom is the site of the shrine of sister of Imam Ali ibn Musa Rida, the eighth Shi'ite Imam.
The city is a significant destination of pilgrimage.