Alzheimer’s disease (AD) is the most common type of dementia and is currently incurable, and mitogen-activated protein kinase (MAPK) p38 is implicated in the pathogenesis of AD. p38 MAPK inhibition is considered a promising strategy against AD, but there are no safe inhibitors capable of penetrating the blood–brain barrier. Earlier, we have shown that mitochondria-targeted antioxidant plastoquinonyl-decyltriphenylphosphonium (SkQ1) at nanomolar concentrations can prevent, slow down, or partially alleviate AD-like pathology in accelerated-senescence OXYS rats. Here we confirmed that dietary supplementation with SkQ1 during active progression of AD-like pathology in OXYS rats (aged 12–18 months) suppresses AD-like pathology progression, and for the first time, we showed that its effects are associated with suppression of p38 MAPK signaling pathway (MAPKsp) activity. Transcriptome analysis, western blotting, and immunofluorescent staining revealed that SkQ1 suppresses p38 MAPKsp activity in the hippocampus at the level of expression of genes involved in the p38 MAPKsp and reduces the phosphorylation of intermediate kinases (p38 MAPK and MK2) and a downstream protein (αB-crystallin). Thus, the anti-AD effects of SkQ1 are associated with improvement in the functioning of relevant signaling pathways and intracellular processes, thus making it a promising therapeutic agent for human AD.