Lay a fabric or plastic dropcloth on the floor beneath the area of interior brick you intend to clean. The dropcloth catches moisture and debris to prevent it from making a mess on the floor.
Pour 2 capfuls neutral stone cleanser in a bucket and add warm water in the amount directed on package instructions. Mix the solution to create soapy water.
Dip a scrub brush in the mild cleanser. Start at the top of the wall and scrub your way down. Rinse the scrub brush frequently and apply more soap solution as needed.
Fill a bucket with warm water. Rinse the brick wall by scrubbing it with plain water. Press a dry cloth into the brick to remove excess moisture then allow the wall to air dry.