The scene all played out earlier Friday in Canada ... where Raptors president Masai Ujiri was helping unveil a basketball court that a local foundation had helped renovate.

During the festivities, Ujiri announced he had a surprise for Carter -- revealing his team was going to hang the former superstar's No. 15 threads in its rafters at Scotiabank Arena.

"On behalf of all of us," he said, "we say congratulations, Vince. First jersey to go up."

Check out the video, almost immediately after the words left Ujiri's lips ... Carter began to tear up. In fact, he got so overwhelmed, he had to walk away to collect himself.

At one point, he put his hands on his knees to catch his breath.

After a few moments, he shared a big embrace with Ujiri -- all while a crowd at the court cheered the two on.

The retirement ceremony is slated to go down in November ... but, surprisingly, it's not the only team that's going to put his uni away forever -- the Nets will also bestow the honor on the 47-year-old in January.