A 22-year-old student fell Sunday morning while climbing a bell tower at Fordham University with friends to snap pictures of the skyline, according to authorities.

The woman, whose name was not released, was “extremely critical” after the 40-foot fall, cops said.

The group of seniors climbed the Keating Hall clock tower at about 3 a.m. when the woman fell through an opening on the first landing of the tower and tumbled inside the structure, striking her head on the ground, cops said.

Students told The Post it was a “rite of passage” among seniors to climb the tower, touch the bell and taking photos outside one of the top windows.

“I heard they were just getting a better view of the city,” a senior student, Anne, told The Post. “I think they were posting on Instagram when it happened.”

The news spread quickly to fearful parents, who warned their kids to steer clear of the structure.

“My mom texted me this morning and said, ‘stay out of the bell tower!” said Grayson Brown, 19, a freshman computer science major from Bethesda, Maryland.

EMS rushed the injured student to St Barnabas Hospital, where she was in critical condition.

“Access to that tower is always locked,” school spokesman Bob Howe told The Post. “University officials are investigating how the students gained access to the tower.”

But a student said it is often open at night.

“The doors aren’t always locked. They’re unlocked at night when they’re cleaning. They are always doing some kind of cleaning or renovation,” said a senior named Anne who declined to give a last name.

It was too early to tell whether the door was open or the lock had been tampered with, Howe said.