Final answer:
The Golgi apparatus is responsible for organizing, modifying, and packaging proteins into secretory vesicles, which are then transported within the cell or secreted.
Step-by-step explanation:
The organelle that packages proteins into secretory vesicles is the Golgi apparatus. The Golgi apparatus receives proteins from the rough endoplasmic reticulum (RER), then organizes, modifies, and packages them into vesicles. These vesicles may be transported to other areas of the cell or may be exported from the cell through exocytosis. The process of packaging can also involve the creation of new lysosomes or the addition of proteins to existing ones. This process is critical for the proper sorting and delivery of proteins throughout the cell and for secretion out of the cell.