This study investigated the association between parent and child sodium and potassium intakes using data from the 2016 Aomori Prefectural Health and Nutrition Survey. We analyzed one day dietary record data of 103 mothers, 94 fathers, 51 children aged 1–3 years, 39 children aged 4–6 years, 91 children aged 7–14 years, and 56 children aged 15–19 years. We also examined the association of sodium and potassium intake between co-habiting grandparents and their grandchildren. After adjusting for covariates, the total daily sodium intake in mothers was positively associated with that in children for every age group. Potassium intakes by the mothers during breakfast and dinner were positively associated with those in children aged 1–3, 4–6, and 7–14 years. The associations in sodium and potassium intakes between fathers and children were weaker. In addition, these associations were similar to those between the sodium intakes of grandchildren and their grandparents. The association between mother and child sodium and potassium intakes at breakfast and dinner was related to the consumption of similar foods, which suggests the importance of home environment in influencing total dietary sodium and potassium intake in Japanese people.