Cops say Sydney went to the campus clock tower with her friends at around 3am.
"I know you join me in keeping Sydney, and her family and loved ones, in your thoughts and prayers", Father McShane also said, reported the New York Times.
It is not clear how exactly she lost her footing but she fell through an opening in a landing.
University officials are looking into how the students gained access to the tower as the door was supposed to be locked.
A 22-year-old university student has died after falling 12m from a campus tower she had climbed to allegedly take pictures for social media.
A mass was scheduled to be held for Monfries on Sunday evening at Fordham University Church. McShane says the school plans to award the student a bachelor's degree posthumously.
At 6:49 p.m., Joseph M. McShane, S.J., announced to the Fordham community that Monfries had died.
Eventually, she was airlifted out through a window then lowered to the ground to be taken to the hospital where she was pronounced dead.
A student, named only as Dave, who met Sydney and her friends hours before the tragedy, said: "My roommate was with them". "There are no words sufficient to describe the loss of someone so young and full of promise - and mere weeks from graduation", he wrote. "I don't think they went up there with the intent thinking that it would be possible to fall". Monfries was with a group of seniors.
Students said climbing the tower, touching the bell and taking photos of the sweeping views, were part of a senior-year "rite of passage", according to the paper.
Access to the tower is restricted, a university spokeswoman told the Times. "But right now they're just trying to process this tremendous loss" while being "very appreciate of all the family and friends who've come around to support them", the friend said.
"They're unlocked at night when they're cleaning", the student claimed.
For many Rose Hill students, the allure of the clock tower has become irresistible.
Some students said climbing the tower is a campus tradition, while others said some climb for the view.