There is apparently no official canon, as mentioned in this wikia article:
Unlike many other franchises, the Mario franchise and its many spin-off series do not have an officially recognized canon. Therefore, arguments over canonicity (canon vs. non-canon) are purely speculative.
This is supported in various other places, as well. See here:
The Super Mario series has no officially recognised canon
the Mario series in general has no sense of canon or continuity
During the 30th anniversary of the Super Mario series, however, it seems that Nintendo released what some considered a "canon list" of the Super Mario games. This list is mentioned in this post:
Nintendo updated its Japanese Super Mario Bros. 30th anniversary site today. What came out of it was only something us Mario fanboys can fanboy about. Nintendo released a history of the Super Mario series. In it to my surprise were the Super Mario Land games!
However, it seems that this list is not widely recognized as a real list of canon entries in the series. In fact, some even see it as more of a joke to play on the fact that there is no official Mario canon, which Shigeru Miyamoto has done in the past.
From this thread that says Miyamoto "revealed" that Mario and Luigi's last name was "Mario" the whole time, one of the top comments asserts that this is purposefully false information:
Miyamoto's gone on record before that it's not their last name, and that they don't even have last names at all. It's certainly not the first time he's offered contradictory authoritative statements on the Mario world. I like to believe that Miyamoto is just subtly mocking anyone who believes Mario "canon" is a thing.
After searching for this, I found the quote here from an interview with Miyamoto:
“This is an old story, but Hollywood did a film version of the Mario Bros. many years back. There was a scene in the script where they needed a last name for the characters. Somebody suggested that, because they were the Mario Bros., their last name should be Mario. So, they made him “Mario Mario.” I heard this and laughed rather loudly. Of course, this was ultimately included in the film. Based on the film, that’s [how] their names ended up. But, just like Mickey Mouse doesn’t really have a last name, Mario is really just Mario and Luigi is really just Luigi.”
Thus, that "big reveal" was actually Miyamoto saying that the (objectively terrible) Super Mario Bros. movie made Mario's last name Mario canon (which it did not).
Thus, it seems safe to assume that the list of Super Mario games does not reflect canonicity, either, and that the Super Mario series remains canon-less.