In recent times, climate change has become more evident than ever, and measures to slow down its negative effects are imperative for the future of the world. The scientific and economic communities of countries around the world, under the force of international climate agreements, are identifying solutions to reduce greenhouse gas (GHG) emissions by establishing appropriate measures and developing new strategies. In the context of these objectives, the effort to identify eco-sustainable practices for the construction industry is growing significantly. Recently, much research has focused on solutions for producing green building materials, as well as applying circular economy principles to achieve a balance between anthropogenic emissions and absorptions by greenhouse gas absorbers. The relevant indicators of the level of achievement of these major objectives can be identified, already from the construction design phase, with the help of Life Cycle Assessment (LCA) analysis. This paper presents a series of environmental impact analyses for an eco-friendly solution of precast concrete masonry blocks. Ecological concrete is manufactured with aggregates from biological waste resulting from hemp crops. Impact assessments were performed with the SimaPro 9.5 software application. Research has shown that in the production chain, which includes the materials resulting from the recycling and reuse of hemp concrete blocks, the contribution to the effort to achieve neutrality in terms of global warming is significant. The Cradle-to-Cradle scenario revealed that the recycling of hemp concrete masonry blocks at the end of their use, for a functional unit of 0.5 m3, has a GHG emission of 33.5228 [kg CO2-eq] and CO2 uptakes can reach the negative value of −53.8397 [kg CO2-eq]. Thus, the balance of GHG emissions is negative, with values of approximately −20.3169 [kg CO2-eq]. The LCA analyses also reflect a decreased damage to human health, natural resources, and biodiversity when hemp concrete is used for masonry blocks.