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In this note we obtain the existence and the uniqueness of the solution of a variational inequality associated to the degenerate operator $$Lu=-\sum _{i,j=1}^n{(a_{ij}(x)u_{x_i}+d_{j}u)}_{x_j}+\sum _{i=1}^n{b}_i{u}_{x_i}+cu$$ assuming the coefficients of the lower terms and the known term belonging to a suitable degenerate Stummel-Kato class. The weight $w$, which gives the degeneration, belongs to the Muckenoupt class $A^2$.