The objectives of this study were: (a) to determine asymmetries, both lower limb (LL) and upper limb (UL), in Chilean older adults, and (b) to relate asymmetries to FA in both LL and UL. Forty-one older adults voluntarily participated in this study (mean ± standard deviation [SD]: age 72.0 ± 8.0 years, LL asymmetries 13.78 ± 14.87%, UL asymmetries 10.70 ± 8.85%, FA 40.35 ± 16.26 points). The variables were: (1) asymmetries of LL and UL, assessed through a force platform and handgrip, respectively; (2) FA, assessed through the Latin American Group for Maturity (GDLAM) and the GDLAM index of autonomy (GI) protocol. The relationship between the variables was performed through Spearman’s correlation. The analysis showed that 39% of the participants presented asymmetries above 15% in the LL. Likewise, this 39% of older adults presented a lower FA than their peers with asymmetries below 15% in the LL (≤15%: 35.64 ± 12.26 points vs. >15%: 47.69 ± 19.23 points, p = 0.003). The analysis showed a small correlation between LL and GI asymmetries (r = 0.27, p = 0.07) and a small but negative correlation between UL and GI (r = −0.21). The mean values of asymmetries of both LL and UL are within ‘normal’ parameters. However, several older adults were identified as being at risk. In parallel, older adults who presented a higher level of asymmetries in LL showed a lower level of FA.