Many of the students staying there were thought to be in their rooms at the time of the collapse as there were no lessons on Sunday.
A legislative assembly member said at the scene that some of the trapped students had been making calls from under the rubble.
Eyewitnesses told local media that another building beside the hostel had also collapsed.
Chief Minister of Delhi Rekha Gupta said an adjacent building had been evacuated “as a precautionary measure”.
“Every possible effort is being made to safely rescue those trapped,” she added.
Delhi Police said the building had only been 40 or 50 years old.
The owner of a nearby shop told news agency ANI that it was under a 100-year lease and that the leaseholder had undertaken excavation work in the basement to increase their income.
“They strengthened the upper building, but the pillars below were weak,” he said, noting that the construction workers had also been buried.
The National Students’ Union of India called on the government to investigate the cause of the collapse and hold anyone found responsible to account.
“Negligence with the safety of students and common people will not be tolerated at any cost,” it said.
Police are searching for the owner of the building, Times of India reports.
