Background: Albuminuria and albumin excretion rate (AER) are important risk factors for chronic kidney disease (CKD) development. Despite the extensive evidence of the influence of sodium and potassium on cardiovascular health, the existing evidence regarding their impact on albuminuria and kidney disease is limited and inconsistent. Our study aimed to assess the correlation between urinary sodium and potassium excretion, and the sodium-to-potassium ratio (Na/K ratio) with impaired kidney function, particularly the AER and albuminuria. Materials and Methods: Data were collected from the Lithuanian NATRIJOD study. A total of 826 single 24-h urine samples from individuals aged 18 to 69 were collected and analyzed for their sodium and potassium levels, Na/K ratio, and AER. Albuminuria was defined as an AER exceeding 30 mg/24 h. Results: The participant mean age was 47.2 ± 12.1 years; 48.5% of the participants were male. The prevalence of albuminuria was 3%. Correlation analysis revealed a positive correlation between AER and urinary sodium excretion (rs = 0.21; p < 0.001) and urinary potassium excretion (rs = 0.28; p < 0.001). In univariate linear regression analysis, sodium and potassium excretion and the Na/K ratio were significant AER predictors with β coefficients of 0.028 (95% CI: 0.015; 0.041; p < 0.001), 0.040 (95% CI: 0.003; 0.077; p = 0.035), and 1.234 (95% CI: 0.210; 2.259; p = 0.018), respectively. In the multivariable model, only urinary sodium excretion remained significant, with a β coefficient of 0.028 (95% CI: 0.016; 0.041). Potential albuminuria predictive factors identified via univariate logistic regression included urinary sodium excretion (OR 1.00; 95% CI: 1:00; 1.01) and the Na/K ratio (OR 1.53; 95% CI: 1.11; 2.05). However, these factors became statistically insignificant in the multivariate model. Conclusions: Urinary sodium and potassium excretion and the Na/K ratio are significantly associated with kidney damage, considering the assessed 24-h albumin excretion rate and presence of albuminuria content.