Wall-mounted planters, big or small, need to be securely mounted on any wall. Always remember to use "pan head" or hex head "lag" screws to hang pots. These screws provide a lip to keep your pot from falling off, unlike screws with a tapered profile.
Your local hardware store will be familiar with these terms. Never fully tighten a screw on a ceramic or glass wall pot, as both materials need to be able to expand and contract with temperature. If you want to install the pot into drywall, you will need the appropriate screws and possibly a drywall anchor, depending on the weight of the wall pot and the desired location.
Make sure you read the instructions that came with your wall planter and take note of any recommendations they make, including weight requirements. If installing the planter in concrete or masonry, use anchors or screws designed for the task.