This study compared the wound-healing response and osteogenic gene expression profile of osteoblasts exposed to pediatric-equivalent concentrations of dexmedetomidine (DXMT) and propofol (POF). Human osteoblast-like SAOS-2 cells were assigned to control, low- and high-dose DXMT and POF groups based on pharmacokinetically derived free-drug levels. Scratch-wound closure was quantified over 24 h, and expression of osteogenesis- and cytoskeleton-related genes (RANKL, RUNX2, SP7, BMP2, VIM, VCL, OCN, ALP) was measured by SYBR Green quantitative Polymerase Chain Reaction (qPCR). Normality was assessed using the Shapiro–Wilk test, and group differences were analyzed with two-way ANOVA followed by Tukey’s multiple comparisons test (p < 0.05). All groups demonstrated complete scratch closure by 24 h, with no differences at 6 h. At 18 h, POF did not differ from the control, whereas DXMT significantly accelerated closure at both doses in a dose-dependent fashion. High-dose DXMT significantly increased VIM (3.95 ± 3.12, p = 0.0144) and BMP2 (2.28 ± 0.70, p = 0.0002) expression, while RUNX2, SP7, and RANKL remained comparable to controls. ALP (1.68 ± 0.40, p = 0.0005) and OCN (3.31 ± 0.35, p = 0.0108) were significantly elevated only in the high-dose DXMT group, whereas POF showed no significant effects. At clinically relevant concentrations, DXMT was associated with enhanced scratch closure and increased expression of selected osteogenesis- and cytoskeleton-related genes in SAOS-2 cells, whereas POF showed limited effects under the tested conditions. These findings suggest that DXMT may influence early in vitro cellular responses relevant to bone healing and should be further validated in functional differentiation models and in vivo studies.