The m-th Cullen number C_m is a number of the form m2^m + 1 and the m-th Woodall number W_m has the form m2^m - 1. In 2003, Luca and Stănică proved that the largest Fibonacci number in the Cullen sequence is F₄ = 3 and that F₁ = F₂ = 1 are the largest Fibonacci numbers in the Woodall sequence. A generalization of these sequences is defined by C_m,s = m s^m + 1 and W_m,s = m s^m - 1 for s > 1. In this paper, we search for Fibonacci numbers belonging to these generalized Cullen and Woodall sequences.