  The tensor product of $\mathbb{A}^1$-invariant sheaves with transfers
introduced by Voevodsky is generalized to reciprocity sheaves via the theory of
modulus presheaves with transfers. We prove several general properties of this
construction and compute it in some cases. In particular we obtain new
(motivic) presentations of the absolute K\"ahler differentials and the first
infinitesimal neighborhood of the diagonal.
