They said they have arrested a 31-year-old patient from the hospital's psychiatric ward.
Police said they took him into custody after he allegedly tried to kill a 71-year-old patient at the hospital on Friday.
The investigation was transferred from the hospital to the Montreal police homicide squad.
Montreal police Const. Daniel Lacoursière said no arrests have been made in the two deaths, but authorities are investigating a possible connection between the suspect and the double homicide.
Two elderly people were suffocated at the Notre-Dame Hospital this month. One death happened on June 16 and the other occurred last Thursday.
Yvan Gendron, the hospital's associate director general, said the news of the deaths was delayed because families were being advised.
He called the deaths "isolated cases" and "unique," but added that if security changes are needed, the hospital will make them.
He also lauded the "vigilance" of hospital staff, crediting staff for alerting police "about two deaths from what appeared to be natural causes in the same period."
Police said they were informed by staff about the deaths when they went to investigate the attack on a patient.
Paul Brunet, head of the council for the protection of Quebec patients, said he is worried that the deaths were not made public sooner.
"Had it not been for the police or the media, maybe we would have never heard of it," said Brunet. "My understanding is that Notre-Dame is not that adapted to these kinds of patients and they probably tried to admit a patient that should have been admitted elsewhere."
The suspect is in custody and will undergo a psychiatric evaluation.