No, there are a variety of ways to build strength without using a dumbbell, kettlebell, or barbell. For instance, body-weight exercises are a convenient, effective way to improve muscle mass. Do a few sets of push-ups, squats, lunges, and bear crawls to target muscles throughout your whole body.
You might also consider doing yoga or Pilates, which can also build strength. Poses such as Downward Facing Dog, Tree, Warrior II, and others build muscle strength and stability.