Police believe the children - Kara Johnson, 1, and Aiden Johnson, 3 - are in the company of their 34-year-old father, Zachary Johnson.
Family members and police are concerned for the children's safety.
The children's parents are divorced, police said.
The children's mother last saw the kids on Wednesday at about 5:45 p.m.
Investigators have checked hotels in the Timmins area and spoken to family members and friends, but have been unable to locate the children and their father.
Police said it's possible the children and Zachary Johnson may be travelling to Ottawa, Saint Sauveur, Que., or Nova Scotia, although the vehicle he was driving was found broken down near Westmount Avenue and University Street in Timmins.
Zachary Johnson is described as white, five-foot-10 and skinny with short and curly dark brown hair with some grey, grey/green eyes and scruffy facial hair.
He requires glasses, but is currently not wearing them, police said.
Aiden Johnson is three-foot-six with a stocky build, light brown hair that is medium in length, and blue eyes. He was last seen wearing black and red Oshkosh snow boots with two Velcro straps and a white winter jacket with blue and black rockets and spaceships on it, police said.
Kara Johnson is two feet tall with a petite build, light brown short hair with bangs, fine hair and hazel eyes. She was last seen wearing a turqoise one-piece baby sleeper with a bunny rabbit on the front, police said.
At the age of one, Kara Johnson can say a few words, including "Dora," "grandma" and "grandpa," police said.
Anyone with information about the Johnsons' whereabouts is asked to call 911 immediately.
The Amber Alert is scheduled to end at 10 a.m. unless an extension is requested.