The concept of circular economy is based on the reintegration of materials typically viewed as waste back into the production cycle. For the construction industry, the brick is representative of the new constructions, but also it can be a good example of circularity. In this study, the feasibility of reusing brick waste by alkaline activation in metakaolin-based geopolymer binders and mortars was examined, and its effect on their physical and mechanical properties was evaluated. Sodium hydroxide 10 M and sodium silicate (SiO2:Na2O = 3.4, 35 wt.%), in a 1:2 ratio, were used as alkaline solution. The influence of curing condition was evaluated by using different temperatures and time for the geo-polymerization process to take place. In particular, geopolymer samples were prepared using two different curing temperatures (30 and 60 °C); the samples were cured for 24 h in the oven and tested at least after 28 days. In the experimental recipes, metakaolin was gradually replaced by brick waste powder up to 60% by weight with an increment of 10%. A replacement of 20% metakaolin by the brick waste powder in geopolymer paste did not substantially reduce the uniaxial compressive strength with respect to the geopolymer made up of metakaolin only. Replacements with major amount of brick waste powder decrease the compressive strength of the geopolymer paste. As regards to geopolymer mortars, made up of geopolymer paste and river sand in 2:3 ratio by weight, the uniaxial compressive strengths reveal an interesting increasing for substitution of sand aggregate with brick waste particles. Curing at low temperature promotes a slow geo-polymerization rate, while increase in temperature quickly favored the strength development. The results revealed that the maximum compressive strength was obtained at a temperature of 60 °C due to the high density of geopolymer matrix. The longer the curing time, the higher strengths are obtained. The obtained results demonstrate a potential value for the adding of brick waste to the production of geopolymer binders and mortars, even in the light of the rather interesting physical and mechanical properties.