Up to Four Days
After a certain period in the fridge, food will start to grow mold or bacteria that can be harmful to your health, but keeping leftovers in the fridge is usually safe for up to four days.
Use your Judgment
You may want to use the zucchini before four days are up, though, depending on what you're planning to use it for. If it's going into a quiche, for example, the texture and color does not matter as much, but if you want to use the zucchini raw in a salad, keep an eye on it to make sure it is not going brown or soft.
Use the prepared zucchini within four days after you store it in the fridge. If you intend to use it without cooking it, consider using it even sooner than this.