Research has shown that educational robotics can be an effective tool to increase students’ acquisition of knowledge in the subjects of science, technology, engineering, and mathematics and promote, at the same time, a progression in the development of computational thinking (CT) skills in K–12 (kindergarten to 12th grade) education. Within this research field, the present study first sought to assess the effect of a robotics laboratory on the acquisition of CT-related skills in primary school children. The study also aimed to compare the magnitude of the effect of the laboratory across third- and fourth-grade students. For the purpose of the study, a quasi-experimental post-test-only design was adopted, and a group of 51 students, from third- and fourth-grade classrooms, participating in the robotics laboratories, were compared to a control group of 32 students from classrooms of the same grades. A set of Bebras tasks was selected as an overall measure of CT skills and was administered to children in both the intervention and control groups. Overall, the results showed that programming robotics artefacts may exert a positive impact on students’ learning of computational thinking skills. Moreover, the effect of the intervention was found to be greater among third-grade children.