At ambient pressure and zero field, tetragonal CeAuSb2 hosts stripe antiferromagnetic order at T_N = 6.3K. Here, we first show via bulk thermodynamic probes and x-ray diffraction measurements that this magnetic order is connected with a structural phase transition to a superstructure that likely breaks C₄ symmetry, thus signaling nematic order. The temperature-field-pressure phase diagram of CeAuSb₂ subsequently reveals the emergence of additional ordered states under applied pressure at a multicritical point. Our phenomenological model supports the presence of a vestigial nematic phase in CeAuSb₂ akin to iron-based high-temperature superconductors; however, superconductivity, if present, remains to be discovered.