Long-term monitoring of respiratory rate (RR) is of great importance in people suffering from sleep-related breathing disorders (SBDs). Instrumented mattresses are gaining the attention of several research groups to monitor this vital sign. Among the existing sensing techniques, fiber Bragg grating sensors (FBGs) show promise in this arena. In this article, we presented a novel FBG-based smart mattress to monitor RR over time. The proposed measuring system consisted of 13 sensing elements (SEs) based on FBGs encapsulated in soft biocompatible rubber, totally embedded in multiple silicone layers. Compactness, robustness, and user comfort are the main advantages of our solution. The mattress size and the arrangement of the 13 SEs were chosen to allow monitoring subjects with different anthropometric parameters and taking up different sleeping postures. Before the overall system integration, each SE was subjected to static and dynamic metrological characterization, a process often overlooked in fiber-optic-based mattresses. Results showed a mean sensitivity to force equal to 14 pm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\cdot \,\,\text{N}^{-1}$ </tex-math></inline-formula> and a mean percentage hysteresis error always lower than 18%. The feasibility assessment of the system in RR monitoring was carried out on five healthy volunteers taking up common sleeping postures (i.e., supine -S-, right side -RS-, left side -LS-, and prone -P-) under two breathing conditions (i.e., quiet breathing -QB-, and tachypnea -T-). RR estimation showed a mean absolute error (MAE) always lower than 0.65 breaths/min. The promising findings proved the capability of our smart mattress in monitoring RR over time, encouraging the investigation of its performance in real-world scenarios.