Superfield formulation of the \(\mathbb {Z}_2^2\) -supersymmetry is developed for the minimal case. The main obstacle of the use of superfields in the \(\mathbb {Z}_2^2\) -graded theory is that the integral over the minimal \(\mathbb {Z}_2^2\) -superspace proposed so far imposes unphysical relations on the physical fields. A new integration is introduced to overcome this difficulty and it allows us to construct \(\mathbb {Z}_2^2\) -supersymmetric action in a way analogous to the standard supersymmetry. The resulting action is defined on the two-dimensional Minkowski space and has very general interaction terms. Moreover, it gives a \(\mathbb {Z}_2^2\) -graded extension of many two-dimensional theories, especially integrable systems such as sine-Gordon, Liouville equations.