The present study evaluates the possibility of producing alkali-activated green building bricks through the application of geopolymerization technology incorporating various solid waste materials. Solid bricks were prepared in accordance with official Vietnamese product standards using fly ash (FA), an industrial byproduct, as the main binder material, which was activated by a strong sodium hydroxide (NaOH) solution. Unground rice husk ash (URHA) was used as a partial fine aggregate substitution (0%–45%) in order to provide a new use of this waste material. After casting, the brick samples were stored at room temperature until the ages required for testing. These samples were checked for dimensions and visible defects. The effects of URHA content on the engineering properties of the bricks, including compressive and flexural strengths, water absorption, bulk density, average weight, and void volume, were also investigated. Experimental results showed that the brick samples exhibited good engineering properties that well conform to the official Vietnamese standard. Compressive strength and flexural strength ranged, respectively, between 9.2–20.8 MPa and 3.2–5.3 MPa. These results demonstrate a great potential for using FA and URHA in the production of green building bricks.