We consider a two-scale parabolic problem describing the water-induced swelling for a class of porous materials with elongated internal structures. The system of evolution equations we are considering here consists of a parabolic equation describing the evolution of the moisture content into a macroscopic domain coupled in a two-scale fashion to a free boundary problem capturing a microscopic swelling process. The macroscopic domain is a three-dimensional object (the target porous material), while the microscopic domains are a stack of elongated pores modeled as one-dimensional halflines connected at an edge to the macroscopic domain. By imposing a flux boundary condition at the edge of each pore, we allow the moisture content to intrude into the respective microscopic domain. In this work, we prove the existence and uniqueness of a solution to our two-scale problem. One key ingredient in our proof is the guarantee that the microscopic solution is measurable with respect to variable pointing out to the macroscopic domain. By using the Banach’s fixed-point theorem, we establish the local-in-time well-posedness of our two-scale problem.