Expansive concrete is used for chemical prestressing. Its essential ingredient is expansive calcium sulfoaluminate (CSA) cement. Based on previous research, expansive concrete must be cured underwater for a minimum of three to four weeks to ensure full expansion. It is evident that such a long period is not practical for the construction industry. Therefore, this paper investigates internal curing with superabsorbent polymers (SAP) as an alternative approach. The first step was to determine the absorption rate and potential long-term storage capacity of SAP by the “tea-bag method” using specifically extracted CSA pore solution as the absorption medium. Based on these findings, the SAP and the predetermined amount of curing water were added “on top” of an established expansive concrete mixture. In this parameter study, different amounts of SAP and water additions were tested. After demolding the specimens, curing was continued in standard laboratory climate, and expansion was measured on selected days over a 21-day period. Finally, flexural and compressive strengths were determined. Results illustrate that the SAP can, indeed, sustain the expansion process. However, the achieved expansion was less than that of the SAP-free reference cured underwater. Besides, a decrease in strength was observed with increasing SAP dosages and internal curing water, which is in line with trends of ordinary concrete. However, curing under ambient air conditions instead of underwater with a still acceptable degree of expansion may prospectively be beneficial for practical applications from procedural, labor, and cost perspectives.