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By combining theorems of Drinfeld and Strauch, we show that the monodromyrepresentation on the special fibre of a Drinfeld modular variety, with levelnot divisible by the characteristic, is surjective. We illustrate this resultin the special case of Drinfeld $\mathbb{F}_q[t]$-modules in level $t$, andapply this to show that the Kronecker factors of a Drinfeld modular polynomialin rank $r$ are irreducible.

The generic monodromy of Drinfeld modular varieties in special characteristic