The eatery, which welcomed Beyond Meat's plant-based burger in just under 4,000 Canadian outlets last month, currently offers an alternative to cow's milk in 30 out of 220 stores in the Buffalo region.
More recently, the food chain announced it was trialing JUST's plant-based, cholesterol-free, egg at selected stores - causing people on social media to pressure Tim Hortons into launching dairy-free milks nationwide.
One Twitter user commented: "All these fast food places bringing in Beyond Meat but still no soy milk.... looking at you Tim Hortons. I WANT ICED COFFEE WITH SOY MILK."
While another said: "Tim Hortons has a vegan sandwich now! It would be NEAT if almond milk or soy milk or oat milk..any non-dairy milk.. could be offered too?"
Last month, a report by Mintel revealed that 23 percent of Brits had used plant-based milk alternatives in the three months to February 2019 - a four percent increase from the previous year.
While cow's milk still made up the bulk of milk sales in 2018 (96 percent), its use is falling - especially among 16-24-year-olds - whose usage declined from 79 percent in 2018 to 73 percent in 2019.