We consider the Carrollian limit of ModMax electrodynamics, namely the limit of vanishing speed of light, for the most general, four-dimensional, duality and conformal invariant electromagnetism. The theory is parameterized by a unique real constant gamma, which remains playing a non-trivial role in the magnetic Carrollian case, while it can be removed in the electric Carrollian contraction, and we therefore focus in the former. Applying the technique of Lie point symmetries, we obtain that the magnetic limit is invariant under the Carrollian group, as well as under the local translation in Carrollian time x0 -> x0 ' = x0+f (xi) and xi -> xi ' = xi, with f being an arbitrary function. A diagonal part of the symmetries span the Conformal Carroll algebra of level 2, ccarr2 in four dimensions. Two additional internal symmetries remain in the Carrollian limit of ModMax standing for the conformal invariance of the theory, as well as the invariance under duality transformations.