Walking a dog is one of the few exemptions to the rules.
The couple's unusual arrangement was discovered at 9pm on Saturday, shortly after the rules came into effect.
Isabelle Gendron, of the Sherbrooke Police Department, told the local newspaper La Tribune the couple "did not co-operate with the police at all" and the pair were fined CA$1546 ($1682) each.
The curfew is needed to prevent gatherings that have fueled the rampant spread of the virus, Quebec Premier Francois Legault said. The French-speaking Canadian province has a population of more than 8.4 million.
"The situation is critical and a shock treatment is needed," Legault said in a Facebook post.
"Our hospitals are filling with Covid-19 patients. Hundreds of people are in intensive care, fighting for their lives. Tens of people die every day."
The curfew has seen sharp resistance from some.
Just before the curfew was set to take effect, a few dozen people walked through the streets of Montreal's Plateau district, chanting "freedom" as five police cruisers with lights flashing trailed behind them. A helicopter hovered overhead, and police cruisers lined the streets.
-Additional reporting, AP