The relationship between social engagement and handgrip strength has been underexplored. Further, no prior research examined a plausible reciprocal association between them. The study employed the seven waves of data (2006-2018) from the Korean Longitudinal Study of Aging (KLoSA) survey (7,927 respondents, mean age: 59 years old at wave 1 [71 years old at wave 7], women: 58%). It used ML-SEM, a cross-lagged panel model with fixed effects fitted by structural equation modeling with maximum likelihood estimation. In particular, the ML-SEM examined whether a reciprocal relationship existed between formal social engagement (number of association memberships and frequency of organizational activities)/informal social engagement (frequency of contact with familiar persons) and handgrip strength (the average of the four dynamometer measurements). The empirical analyses identified a systematic reciprocal association between formal social engagement and handgrip strength. Specifically, formal social engagement was positively associated with handgrip strength over time (the number of association memberships standardized coefficient: 0.012*, the frequency of organizational activities standardized coefficient: 0.022***). Conversely, handgrip strength was positively related to the number of memberships (the handgrip strength standardized coefficient: 0.025*) and the frequency of organizational activities (the handgrip strength standardized coefficient: 0.042**). The study thus supports the social causation proposition that formal social engagement in and through diverse associations may be positively associated with handgrip strength. It also validates the health selection argument that handgrip strength may increase the likelihood of formal social engagement.