  The modulus metric between two points in a subdomain of $\mathbb{R}^n, n\ge
2,$ is defined in terms of moduli of curve families joining the boundary of the
domain with a continuum connecting the two points. This metric is one of the
conformally invariant hyperbolic type metrics, which have become a standard
tool in geometric function theory. We prove that the modulus metric is not
H\"{o}lder continuous with respect to the hyperbolic metric.
