Officers are searching the ground and the water, and have deployed a helicopter to aid in the search in Beloeil, which is situated about 35 kilometres east of Montreal.
Police said the case is bizarre.
"One of the parts that is very mysterious is...when you leave without your [bank] cards, without your keys...when you leave your phone and you go, it's suspicious for us," said Insp. Yanic Parent, a spokesman for the Richelieu—Saint-Laurent police.
"We're in front of what seems to be a normal person — no special addictions to alcohol or drugs, no specific past of depression."
Parent said the police force has deployed all its resources to find her, and neighbours are also helping out.
Officers are also searching the Richelieu River because it is so close to her house.
Bau-Tremblay, who is five months pregnant, disappeared Saturday. Police said she had just returned home from a vacation in the Eastern Townships.
A short time later, she left her home on foot alone and never returned.
Some neighbours told CBC they know almost nothing about Cheryl Bau-Tremblay and her partner, except that they moved into the area about a month ago.
Bau-Tremblay stands five-feet-two-inches tall, weighs about 140 pounds and has black hair and blue eyes. She speaks French and has a black tattoo on her wrist.
She was wearing black clothing when she left home.