Decreased appetite is one of the main risk factors of malnutrition. Little is known on how appetite changes during hospitalization and after discharge and how it relates with sarcopenia-related outcomes. We analyzed data of the Hospital-ADL study, a multicenter prospective cohort study that followed 400 acutely hospitalized older adults (≥70 year). Appetite (SNAQ), handgrip strength (Jamar), muscle mass (BIA), mobility (DEMMI), and physical performance (SPPB) were assessed within 48 h of admission, at discharge, and at one and three months post-discharge. The course of decreased appetite was analysed by Generalised Estimating Equations. Linear Mixed Model was used to analyse the associations between decreased appetite and the sarcopenia-related outcomes. Decreased appetite was reported by 51% at hospital admission, 34% at discharge, 28% one month post-discharge, and 17% three months post-discharge. Overall, decreased appetite was associated with lower muscle strength (β = −1.089, p = 0.001), lower mobility skills (β = −3.893, p < 0.001), and lower physical performance (β = −0.706, p < 0.001) but not with muscle mass (β = −0.023, p = 0.920). In conclusion, decreased appetite was highly prevalent among acute hospitalized older adults and remained prevalent, although less, after discharge. Decreased appetite was significantly associated with negative sarcopenia-related outcomes, which underlines the need for assessment and monitoring of decreased appetite during and post hospitalization.