(1) Background: Older people with COVID-19 infection report worse clinical outcomes. There is a paucity of local data and this study aimed to describe the clinical progression of older people admitted to a university hospital in Malaysia with COVID-19 infection. (2) Methods: Older people (≥60 years) admitted with COVID-19 infection confirmed with RT-PCR from 27 February 2020-25 May 2020 were included in this study. Data on patient characteristics, hospital treatment, and inpatient outcomes were collected via hospital-held electronic medical records. Analysis was done to describe the cohort and identify factors associated with inpatient mortality. (3) Results: 26 participants were included (mean age 76.2 years, female 57.7%). All had at least one comorbid condition and half were frail. About 19.2% had non-respiratory (atypical) symptoms; 23.1% had a severe disease that required intensive care unit monitoring; 46.2% were given COVID-19 targeted therapy. Inpatient mortality and overall complication rates were 23.1% and 42.3%, respectively. Delirium on presentation and lower Ct-value were associated with mortality. (4) Conclusions: Older people with COVID-19 infection have severe infection and poor hospital outcomes. Vigilant hospital care is necessary to address their multimorbidity and frailty, along with appropriate treatment for their infection.