Hyperbolic metamaterials (HMMs) have attracted much attention because they allow for broadband enhancement of spontaneous emission and imaging below the diffraction limit. However, HMMs with traditional metals as metallic component are not suitable for applications in the infrared spectral range. Using Ga-doped ZnO, we demonstrate monolithic HMMs operating at infrared wavelengths. We identify the material's hyperbolic character by various optical measurements in combination with theoretical calculations. In particular, negative refraction of the extraordinary wave and propagation of light with wave vector values exceeding that of free-space are demonstrated in the entire telecommunication window. These findings reveal a considerable potential for creating novel functional elements at telecommunication wavelengths.