Meeting the current demand for concrete requires not only mining tons of gravel and sand, but also burning large amounts of fossil fuel resources in cement kilning. Consequently, concrete recycling is crucial to achieving a material-efficient society, especially with the application of various categories of concrete and the goal of phasing out fossil fuels. A comparative life cycle assessment (LCA) is used to assess the engineering material footprint (EMF) and the fossil fuel material footprint (FMF) in closed-loop recycling of three types of concrete: siliceous concrete, limestone concrete, and lightweight aggregate concrete. This study aims to investigate the impact of (i) concrete categories, (ii) methods to model recycling, and (iii) using renewable energy sources on the material footprint in concrete recycling. The results highlight that the concrete recycling system can reduce 99% of the EMF and 66–93% of the FMF compared with the baseline system, in which concrete waste is landfilled. All three recycling modeling approaches indicate that concrete recycling can considerably reduce EMF and FMF compared with the baseline system, primarily resulting from the displacement of virgin raw materials. Using alternative diesels is more sensitive than adopting renewable electricity in reduction of the FMF in concrete recycling. Replacing diesel with electrolysis- and coal-based synthetic diesel for concrete recycling could even increase the FMF, while using biodiesel made from rapeseed and wood-based synthetic diesel can reduce 47–51% and 84–89% of the FMF, respectively, compared to the virgin diesel-based recycling system. Finally, we discussed the multifunctionality and rebound effects of recycling, and double-counting risk in material and energy accounting.