Zen Fedory, a high school teacher, and his girlfriend Krissy Green made the discovery as they were heading to their home in Springfield, located outside of Fredericton.
Fedory said they noticed something moving in the snowbank.
"And it's just this little black dot that I probably would have missed but she didn't. We got a little closer and we saw a little baby cub," he said.
Fedory and Green pulled over and waited to see if there was a mother bear around but there was no sign of her and eventually they decided to call the Department of Natural Resources.
As they were waiting for provincial officials to arrive, Fedory said they heard noises in the woods across the road and soon discovered two more cubs.
When the DNR office arrived, he found a basket and a blanket not far from where the cubs had been.
Fedory said it looked as though someone had dropped the cubs off.
Atlantic Wildlife Institute caring for cubs
Pam Novak, the director of wildlife care at the Atlantic Wildlife Institute in Cookville, said she believes it is possible the bears were dropped off.
"Cause it's an odd place whrere they were found — along the side of a road too so you know something obviously isn't adding up," she said.
Novak said something could have happened to their den or their mother may have been killed.
"They're only three or four pounds, so they're not going to be out foraging, especially with snow cover still on the ground so there's not going to be a lot of activity with bears outside their dens," she said.
Novak said since arriving at the wildlife rescue and rehabilitation centre the bear cubs have been doing well.
She describes them as "quite feisty and lively."
"So now we're just looking to see where we go from here, what the health status is and start putting them on a diet so that we can just start working with them over the next few months," Novak said.
She said she expects the black bear cubs will remain at the Atlantic Wildlife Institute for at least a year before being released back into the wild.