In Michael Freeman's The Photographer's Mind, he mentions that consumer-level ultra-wide angle lenses (which he defines as 24mm and below) for 35mm cameras started being widely produced in the 1960s. This fits with what I can see from researching lens history — the retrofocal lens was imported from cinema use (where it had been invented in the 1930s) in about 1950, and over the next decade became widely available from different manufacturers.
In 1958, the journal Photogrammetric Engineering has an article where, in the context of aerial photography, "ultra wide-angle" is defined as having angular coverage greater than 120°. That'd be something like 12.5mm on the 35mm film frame, or about 8mm on APS-C. But that's a technical application. As the marketers starting trying to sell wider-angle lenses to consumers, the numbers crept up considerably, and I found several instances of companies calling 28mm lenses ultra wide-angle — this Minolta book for beginners, for example.
I also found numerous other references to 24mm as being the cut-off point (like this excerpt from Time-Life's The Camera). So, while the Wikipedia article doesn't (currently) give any sources for its claim, it looks like there's pretty broad consensus.