Umm. Depends. Certainly a separation between modern and classic does exist regardless of the disagreement over where that separation is and what it means. If you mean classic and modern just in terms of dates, then that's highly relative and I'd say anything pre-Wii would could as classic. Wii and onward would basically be modern Zelda, but even the GameCube is pretty old now, so while The Wind Waker, Four Swords Adventures, and The Minish Cap aren't necessarily as classic of titles as the NES through N64 titles, they're still pretty old and the Zelda releases on the GameCube are definitely in the territory of games we distinct look back on.
Usually when I hear the term people are talking about a dividing line in terms of simply how the games play, though. Classic Zelda being the games with more minimal plots, more open exploration, higher difficulty, etc. While modern Zelda is more story-based, linear, and can tend to hold your hand.
In such a case people usually cite The Wind Waker as the turning point, or onward. But the turning point really began in Ocarina of Time. It was the game that started to make Zelda games cinematic. It was the game where exposition and storytelling became prominent. It wasn't overly easy by any means, but it was a much easier game than A Link to the Past. And it's when Zelda started to take on a linear structure, a notion which people like to shoot down because you can, in fact, mess up the order. But to do that, what do you have to do? Leave dungeons before you've completed them, taking the dungeon item elsewhere. It's really clear that Nintendo did not intend for the game to be linear, it was just that they failed to put up functional restrictions to actually stop you. The game still has a linear structure and flows properly when you do things in the intended order, even if they don't have the restrictions to actually force you to do so. It also began the regional separation concept, with you going through localized storylines in specific areas, particularly during the Child Link portion but even during the Adult Link portion as well.
Although... the linearity and storytelling angles also existed in Link's Awakening, so perhaps the divide began somewhere between Link's Awakening and Ocarina of Time instead, but certainly Ocarina of Time is the game that popularized it. And these are still great games that didn't fall into most of the pitfalls I complain about regarding modern titles, so they executed the trends they started well. But they definitely did start those trends. They're where the formula of most modern Zelda games began. The Wind Waker and Twilight Princess first made the formula pronounced and extreme, but they didn't create it.