H19, a long noncoding RNA (lncRNA), reportedly protects myocardial cells (H9c2 cell line) against hypoxia-reoxygenation- (H/R-) induced injury. Dexmedetomidine (Dex) has an important myocardial protective effect, although its function and mechanism in cardiac ischemia/reperfusion (I/R) injury, especially for senile patients, requires further study. RNA N6-methyladenosine (m6A) is the most abundant endogenous RNA modification. However, the effect of Dex postconditioning on RNA m6A modification has rarely been reported. The aim of this study was to evaluate roles of H19 and m6A modification in Dex postconditioning of aged cardiomyocytes. Hydrogen peroxide (H2O2) was used to induce senescence of H9c2 cells. After 6 h of hypoxia, H9c2 cells were exposed to different concentrations of dexmedetomidine (0, 500 nM, 1 μM, and 2 μM) for 6 h. After knockdown or overexpression of H19 and its downstream gene miR-29b-3p and cellular inhibitor of apoptosis protein 1 (cIAP1), Dex postconditioning experiments were performed to examine effects on myocardial cell injury. Global m6A levels after H/R with or without Dex postconditioning were measured with a colorimetric m6A RNA Methylation Quantification Kit. The mechanism by which RNA m6A methylation regulated genes mediating H19 expression was verified by m6A RNA immunoprecipitation (MeRIP), and the function of Dex postconditioning of aged cardiomyocytes was investigated. Dex postconditioning protected against H/R-induced injury of aged myocardial cells through H19/miR-29b-3p/cIAP1, increased methylation of RNA m6A elicited by H/R, and attenuated H/R-induced injury by suppressing expression of the RNA m6A demethylase gene alkB homolog 5 (ALKBH5). In addition, AKLBH5 regulated the expression of H19, and Dex postconditioning attenuated H/R-induced injury via ALKBH5 in aged cardiomyocytes.