Many elderly patients with COVID-19 are at risk of malnutrition. The aim of our study was to evaluate the risk of malnutrition and sarcopenia in elderly COVID-19 patients with the R-MAPP (Remote-Malnutrition APP). A cross-sectional study of 337 consecutive outpatients ≥65 years who attended the Central Emergency COVID-19 Hospital of Castilla y Leon was conducted. In all patients, the protocol of R-MAPP (Malnutrition Universal Screening Tool MUST and Simple Questionnaire to Rapidly Diagnose Sarcopenia SARC-F) was realized. The mean age was 86.1 ± 8.7 years, with a sex distribution of 167 males (49.5%) and 170 females (51.5%). According to the MUST test, patients with 0 points have a low nutritional risk (n = 50, 14.8%), 1 point a medium nutritional risk (n = 19, 5.6%), and 2 or more points a high nutritional risk (n = 268, 79.6%). The SARC-F questionnaire generates patients with 4 or more points as predictive of sarcopenia (n = 304, 80.2%) and <4 points without prediction of sarcopenia (n = 33, 9.8%). Global mortality was 24.03% (n = 81). The mortality rate was related to the pathological SARC-F score ≥4 (27.1% vs. 3.1%; p = 0.01) and MUST score ≥2 (26.7% vs. 16.4%; p = 0.04). In the logistic regression analysis, only the SARC-F score ≥4 remained as an independent variable related to mortality; odds ratio was 8.34 (95% CI: 1.1-63.8; p = 0.04), adjusted for age, sex, albumin levels, and MUST test. During COVID-19 infection, hospitalized patients at risk of sarcopenia have a high risk of mortality and have a poor nutritional status.