Given two integers \(a\) and \(b\) with \(b\neq 0\) we write \(a\bmod b\) to denote the remainder of the division of \(a\) by \(b\). Following the notation used by J. C. Rosales, P. A. García-Sánchez and J. M. Urbano-Blanco [in Pac. J. Math. 218, No. 2, 379-398 (2005; Zbl 1184.20052)], a modular Diophantine inequality is an expression of the form \(ax\bmod b\leq x\). The set \(S(a,b)\) of integer solutions of this inequality is a modular numerical semigroup. If \(S\) is a numerical semigroup, then the greatest integer \(g(S)\notin S\) is called the Frobenius number. \(S\) is called symmetric if \(x\in\mathbb{Z}\setminus S\) implies \(g(S)-x\in S\). The author proves that \(S(a,b)\) is symmetric if and only if \(a=ut\), \(b=ktt'\) for some positive integers \(t,t',u,v,k\) such that \(ut-vt'=1\) and \(k\mid u+v\).