(1) Background: Epidemiological studies on the relationship between serum copper and hypertension are contradictory. We assessed the relationship between serum copper and blood pressure among adults in the United States. (2) Methods: We divided hypertension into two categories: treated hypertension and untreated hypertension. Linear or logistic regression analysis was applied to investigate the association between serum copper concentrations and blood pressure levels. (3) Results: As compared to quartile 1, the odds ratios (ORs) for untreated hypertension in quartiles 2, 3, and 4 were 1.02 (0.74–1.42), 1.23 (0.88–1.72), and 1.08 (0.74–1.58), respectively, in multivariable analysis (all p > 0.05). In non-hypertension, as compared with quartile 1, the β (95% CI) of systolic blood pressure for quartiles 2, 3, and 4 was −0.92 (−2.07–0.23), −0.05 (−1.30–1.20), and −0.48 (−1.83–0.88), respectively, in multivariable analysis (all p > 0.05). As compared to quartile 1, the ORs for treated hypertension in quartiles 2, 3, and 4 were 1.36 (0.88–2.10), 1.35 (0.87–2.09), and 1.56 (0.98–2.47), respectively, upon multivariable analysis including antihypertensive medication use as a covariate (all p > 0.05). Furthermore, 1SD increase in serum copper was non-significantly associated with 1.16 (0.97–1.37)-fold increased risk of hypertension in multivariable analysis (p = 0.096). (4) Conclusion: In the present study, we discovered that the serum copper concentration was not related with hypertension or blood pressure levels. Antihypertensive drug use may distort the correlation between copper and blood pressure levels. Information on antihypertensive drug use may be taken into account when identifying new risk factors for hypertension.