Purpose Hand grip strength (HGS) is a widely used indicator of overall muscle strength and general health. We computed a polygenic risk score (PRS) for HGS and examined whether it predicted muscle strength, functional capacity, and disability outcomes. Methods Genomewide association study summary statistics for HGS from the Pan-UK Biobank was used. PRS were calculated in the Finnish Twin Study on Aging (N = 429 women, 63-76 yr). Strength tests included HGS, isometric knee extension, and ankle plantarflexion strength. Functional capacity was examined with the Timed Up and Go, 6-min and 10-m walk tests, and dual-task tests. Disabilities in the basic activities of daily living (ADL) and instrumental ADL (IADL) were investigated with questionnaires. The proportion of variation in outcomes accounted for by PRS HGS was examined using linear mixed models and extended logistic regression. Results The measured HGS increased linearly over increasing PRS (β = 4.8, SE = 0.93, P < 0.001). PRS HGS independently accounted for 6.1% of the variation in the measured HGS (β = 14.2, SE = 3.1, P < 0.001), 5.4% of the variation in knee extension strength (β = 19.6, SE = 4.7, P < 0.001), 1.2% of the variation in ankle plantarflexion strength (β = 9.4, SE = 4.2, P = 0.027), and 0.1%-1.5% of the variation in functional capacity tests (P = 0.016-0.133). Further, participants with higher PRS HGS were less likely to have ADL/IADL disabilities (odds ratio = 0.74-0.76). Conclusions Older women with genetic risk for low muscle strength were significantly weaker than those with genetic susceptibility for high muscle strength. PRS HGS was also systematically associated with overall muscle strength and proximal and distal functional outcomes that require muscle strength.