Frailty syndrome (FS) is a condition characterized by a decline in reserves, observed with aging. The most important consequences of the frailty syndrome include disability, hospitalization, fractures, institutionalization, and early mortality. The aim of this study was to identify the most important risk factors for FS in a group of older hospitalized patients in Poland. A total of one hundred and forty-one (78 women, 63 men) elderly patients from the Departments of Internal Medicine of the Medical University of Lodz (Poland) were recruited for this study. Frailty Instrument of the Survey of Health, Aging and Retirement in Europe (SHARE-FI), handgrip strength (HGS), depressive symptoms using the Geriatric Depression Scale (GDS), and functional ability (FA) using the Instrumental Activities of Daily Living (IADL) were assessed. According to SHARE-FI score, participants were divided into control group, frail, and pre-frail patients. Out of all 141 tested patients, FS was confirmed in 55 patients, and pre-frailty was observed in 52 patients. The occurrence of FS in the group of studied patients was related to age (p < 0.001), widowhood (p < 0.001), comorbidities (p < 0.001), heart diseases (p = 0.04), more medications taken (p < 0.001), lower FA (p < 0.001), weaker HGS, and depression (p < 0.001). The strongest positive correlations were between Share-FI score and the number of diseases (rS = 0.31), GDS (rS = 0.32), while negative correlations with IADL (rS = −0.47) and HGS (rS = −0.35). The study shows that FS is associated with age, comorbidities, number of medications taken, and widowhood. The present study has also demonstrated that FA, depression, and especially HGS are essential determinants of FS of elderly hospitalized people.