The lightly dressed baby was left in some leaves near the school's steps early Saturday and spent about two hours alone before a man came by on a bicycle and heard a faint cry, Cpl. Miles Hiebert said.
"He heard a sound that he thought at first was a cat," Hiebert said Monday. "He went by, and then decided on second thought to return and check it out, and it actually turned out to be this baby.
"Luckily, this gentleman did find her and prevented a real tragedy."
The baby was taken to hospital and treated for exposure, and is reported to be doing well, Hiebert said.
Police officers discovered a stroller nearby and later found the mother, who police say had been drinking.
A 28-year-old woman faces charges of abandonment and failing to provide the necessities of life.
The Mounties have more interviews to conduct and have yet to determine why the baby was left alone.
"We may never know. We're certainly going to need to interview the mother and we'll need to interview anyone else who may have witnessed what happened," Hiebert said.
Police have not released the names of the child or the woman facing charges.