It is well known that the quadriceps muscle group is involved in activity during dynamic balance and that dynamic balance tests are an important feedback tool for predicting lower limb injuries. However, the relationship between maximum leg extension strength and performance in the Y Balance Test is not fully known. The aim of this study was to investigate the relationship between unilateral leg extension strength and dynamic balance in healthy young men. The study was conducted as a cross-sectional study. A total of 33 healthy men (mean age ± standard deviation = 21.21 ± 1.24 years) volunteered for this study. The participants’ dynamic balance was determined with the Y Balance Test and unilateral one repetition maximum strength was determined by the leg extension machine. The same side was preferred for strength and dynamic balance measurements. Normalized reach, composite score, and absolute and relative strength values were analyzed for correlations. Linear regression analysis was used to determine whether strength values predicted the results of the Y Balance Test. There was a positive linear correlation between the strength values and normalized reach distances and composite scores (r ranges from 0.466 to 0.757; p < 0.01). The coefficients of determination showed that dynamic balance and strength (absolute and relative) performance are not independent parameters in healthy young men (r2 = 21–57% explained variance). It was also found that strength values (absolute and relative) can predict balance. Our study confirmed the relationship between strength and dynamic balance. It can be said that especially the strength of the lower extremity has an acceptable effect on dynamic balance.