This has happened to me before, too! It used to be that if you planted a big field like this, you'd start losing items. Now, this warning appears a while before you reach the game's limit, so probably your items will be safe but you should still take some precautions -- better safe than sorry and that's a lot of plants.
Take any loose items that you want to keep -- your spare axes and your spare clothes and all the random stuff that characters acquire and put them at least 3 world map tiles away from the edge of your giant field.
Some plants may disappear due to the limit but most of your harvest will be fine. You'll have enough food to eat for years.
When it comes time to harvest, stack the harvested plants neatly, 10000 nettles in a single pile count as one item for the sake of this limit.
In the future, if you leave two blank rows between each row of crops, you won't hit the limit. I like to do cellular automata patterns like the sierpinski triangle for my fields beause this pattern will automatically fill only a third of the space.