The use of plant ash as a sustainable cementitious material in concrete composition is a widely researched subject in the construction domain. A plant studied so far more for its thermal insulation properties, sunflower, was analyzed in this study with regard to its ash effects on the concrete composition. The present research aimed to analyze the effects of a 2.5%, 5%, 7.5%, 10%, 15%, 20%, or 30% volume replacement of cement by sunflower stalk ash (SA), a sustainable cementitious material, on the concrete compressive strength at 28 days and three months, the flexural and splitting tensile strengths, the resistance to repeated freeze–thaw cycles, and the resistance to chemical attack of hydrochloric acid. The elementary chemical composition of the SA and the composites was included also. According to the experimental results, SA decreased the values of the compressive and tensile strength of the concrete, but it improved the concrete behavior under repeated freeze–thaw cycles and under the action of hydrochloric acid. A percent of 10% of SA led to a much more pronounced development of compressive strength over time than conventional concrete (26.6% versus 12%).