We investigate the potential of IAXO and its intermediate version, BabyIAXO, to detect axions produced in core-collapse supernovae (SNe). Our study demonstrates that these experiments have realistic chances of identifying SN axions, offering crucial insights into both axion physics and SN dynamics. IAXO's sensitivity to SN axions allows for the exploration of regions of the axion parameter space inaccessible through solar observations. In addition, in the event of a nearby SN, d ∼ 𝒪(100) pc, and sufficiently large axion couplings, gaγ ≳ 10-11 GeV-1, IAXO could have a chance to significantly advance our understanding of axion production in nuclear matter and provide valuable information about the physics of SNe, such as pion abundance, the equation of state, and other nuclear processes occurring in extreme environments.