We propose two preconditioners based on the fast sine transformation for solving linear systems with ill-conditioned multilevel Toeplitz structure. These matrices are generated by discretizing the two-dimensional nonlocal Helmholtz equations with fractional Laplacian operators via the finite difference method. For complex wave numbers with nonnegative real parts, we give the spectral analysis of the preconditioned matrices. Additionally, we extend the proposed preconditioners and algorithm to address the general cases of the nonlocal Helmholtz equations that feature negative, complex with negative real parts, and variable wave numbers. Numerical experiments also indicate that the proposed preconditioners outperform the existing preconditioners.