Naturally occurring hydrous sulphate minerals bearing rock, sampled from a Martian analogue area, Kachchh, India was investigated for sequestration of metal ions of nuclear significance in view of waste management applications. Structural analyses revealed the presence of alunite group minerals (such as hydronium jarosite, alunite, natroalunite) along with a phyllosilicate mineral—kaolinite in the sample. Sorption performance assessment in batch mode for cesium (Cs) demonstrated the influence of initial sorbate concentration and solution pH on the uptake of metal ions. Equilibrium sorption data upon correlation with the theoretical isotherms showed better agreement with Langmuir model with a monalayer sorption capacity of 26.4 mg g−1 for Cs. Maximum uptake of metal ions in acidic pH is a signature of involvement of structural ions in the sorption process. EDXRF analysis demonstrated the loading of sorbate ions on the surface of sorbent after sorption. The studies highlight that the cation retention potential of naturally available hydrous sulphate minerals bearing rock could be instrumental for possible application of the material as barrier matrix to immobilize metal ions of nuclear importance in acidic conditions.