This study investigates the nonlinear free vibration of thin, fluid-filled cylindrical shells made of hyperelastic material. Utilizing the Mooney-Rivlin constitutive model, the equations of motion are derived via Lagrange’s equation, accounting for potential, kinetic, and damping energy. To ensure a higher level of accuracy and precision in capturing the shell's kinematics, the analysis employs Novozhilov's nonlinear shell theory, which incorporates higher-order geometric terms often neglected in standard analytical approaches. This theoretical framework constitutes the core novelty of the present work, enabling a more rigorous investigation compared to existing studies that rely on simplified shell theories. The multiple-scale method is employed to obtain an analytical solution based on this refined model. Key findings include: (1) the fundamental vibration mode is identified as (1,4), corresponding to one longitudinal half-wave and four circumferential waves; (2) the presence of fluid markedly reduces the natural frequency due to added mass effects; (3) the system generally exhibits hardening behavior, which intensifies with increased fluid content and higher circumferential wave numbers; however, a transition to softening behavior occurs when the shell length is four times the radius (β=0.25); and (4) a weakly hardening response is observed when shell length equals its radius (β=1). Results are validated against finite element simulations in ANSYS and compared with existing literature, offering valuable insights for the design and vibration control of soft fluid-structure systems in applications such as soft robotics and biomedical implants.