The ancestral method of preparing chuño (freeze-dried potato) involves three steps: freezing, soaking, and drying. The objective of this study is to identify the changes in microstructure, in physicochemical properties, and rheology of gels and suspensions of Andean potato starches caused by the procedure used to obtain chuño. A laboratory simulation of the procedure is performed using the potato variety “Rosadita” (Solanum tuberosum ssp. Andigenum). From the tests carried out on the starches extracted from the chuño obtained in the field and in the laboratory, differences phosphate content and gelatinization temperature are found. Marked differences are observed with respect to the control starch in the soluble amylose content, RVA profiles, textural attributes, and dynamic and viscous rheological properties. The chuño starches present greater resistance to granular breakdown. These observations suggest a different hydration, swelling, and gelation mechanism for the Rosadita and chuño starch samples compared to conventional potato starch and at the same time a modification due to the effect of freezing, which is more noticeable in the chuño obtained at −5 °C.