A semiring is an algebraic system \((R,+,\cdot)\) such that \((R,+)\) is a commutative semigroup with identity \(0\), \((R,\cdot)\) is a semigroup with identity \(1\), and ring-like distributivity holds. It is also assumed that \(0r=r0=0\) for all \(r\in R\) and that \(0\neq 1\). A semiring is called an antiring (or zerosumfree semiring) if \(r+s=0\Rightarrow r=s=0\) whenever \(r,s\in R\). For example, the two-element Boolean ring \(B_0\) and the nonnegative real numbers \(\mathbb R^+\) (with the usual \(+\) and \(\cdot\)) are antirings. If \(R\) is a semiring then the set \(M_n(R)\) of \(n\times n\) matrices over \(R\) is a semiring under the obvious operations. The aim of the present paper is to investigate the nilpotent subsemigroups of \((M_n(R),\cdot)\) by generalizing results of \textit{O. Ganyushkin} and \textit{V. Mazorchuk} [J. Algebra 320, No. 8, 3081-3103 (2008; Zbl 1162.20039), Serdica Math. J. 33, No. 2-3, 287-300 (2007; Zbl 1179.20056)] from \(B_0\) and \(\mathbb R^+\) to the case of general commutative antirings. In particular, the following is proved. If \(R\) is a commutative antiring, then the set of nilpotent elements in \(R\) is a nilpotent subsemigroup of \((R,\cdot)\) if and only if \(M_n(R)\) contains a maximal nilpotent subsemigroup. Moreover, in the latter case, every maximal nilpotent subsemigroup is conjugate to the subsemigroup \(UT_n(R)\) of all upper triangular matrices in \(M_n(R)\).