The vice-principal of Modern High School for Girls, Indrani Roy, passed away in Hanoi, Vietnam, early on Monday.
She was on a school trip accompanying students and other teachers.
Roy was in her mid-50s and is survived by her parents and a daughter, who works outside Calcutta.
The school will remain closed on Tuesday as a mark of respect to the teacher.
"Announcing the sudden and shocking demise of Mrs Indrani Roy, our beloved vice-principal, in Hanoi, in the early hours of 16th October '23. May her soul rest in peace. The school will be closed tomorrow, 17th October, as a mark of respect," said the notice on the school website.
The school authorities also sent emails to the parents of students informing them about the death.
The school authorities refused to comment on her death. "We are in a state of shock and you must respect that," a school official said.
Roy had joined the school as an English teacher and was with Modern High School for Girls for over 10 years, said those who had worked with her.
She started with teaching middle school students and then went on to teach senior students right up to Class XII.
A former colleague said she was a "very good English teacher and very organised at what she did".
Before taking over as the MHS vice-principal, Roy was the middle-school coordinator.
Some of the Modern High students and teachers were on a seven-day trip to Hanoi and Ho Chi Minh City. They left last Friday and were scheduled to return this week, a parent said.