For given positive integers a,b,c, and d, we consider the generalized bi-periodic Fibonacci sequence (F_n)_n≥0 defined by the recurrence relation F_n = aF_n−1 + cF_n−2 for n even and F_n = bF_n−1 + dF_n−2 for n odd, with initial conditions F₀ = 0, F₁ = 1. In the present paper, we study the periodicity of (F_n)_n≥0 modulo a given integer m ≥ 2 relatively prime to c and d. We extend some well-known results on the period and the rank of the classical Fibonacci sequence to the bi-periodic case.