"A tree fell on an ambulance, and one of the paramedics was killed," Halifax Regional Municipality spokesman John O'Brien told CBS Radio News.
Another person died in the town of Enfield, northeast of Halifax, also because of a tree falling on a vehicle.
Hundreds of residents were evacuated from low-lying areas and Nova Scotia's power authority warned people to stay indoors Monday because falling trees had knocked down a "terrific" number of still-live power lines.
Halifax, the largest city on Canada's east coast, received the brunt of Juan's punch with wind speeds reaching 89 mph early Monday.
"It was quite a fantastic event," said Carolyn Marshall, spokeswoman at Canada's Hurricane Centre in Dartmouth, Nova Scotia.
In nearby Dartmouth, fierce winds tore off an apartment building's roof and knocked down a wall in a hallway, trapping about three people inside, firefighters said. Police dug through the rubble but reported no injuries.
"We're not sure how stable it is and we're not taking any chances," said fire chief Tim Bookholt. "It's been a busy night. I hope the worst of it is over."
At least 200 residents were evacuated from the four-story building — many of them seniors — and bused to a local hockey arena as a temporary shelter.
In Halifax, the swirling storm system knocked out power to significant areas as downed tree limbs cart-wheeled through city streets and damaged cars.
"Most of the area's without power. There's a lot of trees down, most roads are impassable. They're either blocked with fallen trees or underwater," said O'Brien. "It's very difficult to get around, even for the emergency vehicles. We've had a front-end loader in a couple of cases going ahead of a fire truck trying to clear some debris."
In Nova Scotia's Lunenburg County, crews were using snowplows to clear coastal roads.
The exact number of people left without electricity wasn't known early Monday, but it was "in the thousands," said Margaret Murphy, a spokeswoman for Nova Scotia Power.
Audrey Russell, from the coastal town of Eastern Passage, grabbed a toothbrush, toothpaste, her cat and some clothes and then headed for refuge in a nearby firehouse.
"I was kind of worried, so I didn't want to stay around too long," Russell said.
Juan was downgraded to a Category 1 hurricane earlier Sunday and had lost some of its ferocity by the time it reached cooler waters off Nova Scotia. A Category 1 hurricane has winds ranging from 74 to 95 mph.
In 1996, when Hurricane Hortense brushed past Halifax, the storm surge topped three feet, and winds uprooted trees and left tens of thousands without power. Tropical storms routinely soak Atlantic Canada each summer and autumn, but a full-fledged hurricane making landfall is rare.
Juan arrived a week after Hurricane Isabel hit the U.S. coast, killing 40 people from North Carolina to New Jersey and knocking out electrical service to 6 million customers as far north as New York.
Meanwhile, early Monday morning, Tropical Storm Kate swirled in the Atlantic far from land. Its center was about 970 miles southwest of Lajes in the Azores Islands. Kate had maximum sustained winds near 65 mph and was moving toward the northeast near 14 mph.
The Atlantic hurricane season began June 1 and runs through Nov. 30.