Excess central adiposity accelerates the decline of muscle strength in older people. Additionally, hyperglycemia, independent of associated comorbidities, is related to the loss of muscle mass and strength, and contributes to functional impairment in older adults. We studied the mediation effect of glucose levels, in the relationship between abdominal obesity and relative handgrip strength (HGS). A total of 1571 participants (60.0% women, mean age 69.1 ± 7.0 years) from 86 municipalities were selected following a multistage area probability sampling design. Measurements included demographic and anthropometric/adiposity markers (weight, height, body mass index, and waist circumference). HGS was measured using a digital dynamometer for three sets and the mean value was recorded. The values were normalized to body weight (relative HGS). Fasting glucose was analyzed by enzymatic colorimetric methods. Mediation analyses were performed to identify associations between the independent variable (abdominal obesity) and outcomes (relative HGS), as well as to determine whether fasting glucose levels mediated the relationship between excess adiposity and relative HGS. A total of 1239 (78.8%) had abdominal obesity. Abdominal obesity had a negative effect on fasting glucose (β = 9.04, 95%CI = 5.87 to 12.21); while fasting glucose to relative HGS was inversely related (β = −0.003, 95%CI = −0.005 to −0.001), p < 0.001. The direct effect of abdominal obesity on relative HGS was statistically significant (β = −0.069, 95%CI = −0.082 to −0.057), p < 0.001. Lastly, fasting glucose levels mediates the detrimental effect of abdominal obesity on relative HGS (indirect effect β = −0.002, 95%CI = −0.004 to −0.001), p < 0.001. Our results suggest that the glucose level could worsen the association between abdominal obesity status and lower HGS. Thus, it is plausible to consider fasting glucose levels when assessing older adults with excess adiposity and/or suspected loss of muscle mass.