Periodic π-vacancies in graphene superlattices (GSLs) provide a symmetry-based route to band-gap opening in graphene by modifying the π-band dispersion. However, the symmetry conditions that determine whether a vacancy motif can open a band gap remain unclear. Here, we investigate periodic π-vacancy GSLs using a nearest-neighbor tight-binding model with one p_z orbital per carbon site to identify the symmetry requirements for gap opening. π-vacancies, representing functionalized, substituted, or missing carbon sites, are modeled as site deletions in the π basis, with all hopping matrix elements to and from the deleted sites set to zero. We focus on π-vacancy motifs with C₂ and C₃ point-group symmetry. A 3n × 3n GSL, where n=1,2,3,… is the integer scaling factor multiplying the honeycomb primitive-cell vectors, folds K and K' to Γ and can therefore open a band gap. For C₃-type vacancies, the Dirac cones remain pinned at high-symmetry points and thus stay at Γ in folded 3n GSLs. In contrast, C₂-type vacancies that reduce the global point group of the GSL to D₂ₕ by preserving a pair of perpendicular mirror symmetries, σᵥ ⊥ σ_d, can also constrain the Dirac cones to Γ. When the σᵥ and σ_d mirror planes are absent, the cones are allowed to shift away from Γ to (± Δ q,± Δ q) in the 3n superlattice.