We argue that the existence of the electroweak monopole predicts the existence of the electroweak string in the standard model made of monopole-antimonopole pair separated infinitely apart, which carry the quantized magnetic flux $4 \pi n/e$. We show how to construct such quantized magnetic flux string solution. Our result strongly indicates that genuine fundamental electromagnetic string could exist in nature which could actually be detected. We discuss the physical implications of our result in cosmology.