Practical quantum networks require interfacing quantum memories with existing channels and systems that operate in the telecom band. Here we demonstrate low-noise, bidirectional quantum frequency conversion that enables a solid-state quantum memory to directly interface with telecom-band systems. In particular, we demonstrate conversion of visible-band single photons emitted from a silicon-vacancy (SiV) center in diamond to the telecom O band, maintaining low noise (g^{2}(0)<0.1) and high indistinguishability (V=89±8%). We further demonstrate the utility of this system for quantum networking by converting telecom-band time-bin pulses, sent across a lossy and noisy 50-km deployed fiber link, to the visible band and entangling them with a diamond quantum memory with fidelity F≥87±2.5%. These results demonstrate the viability of SiV quantum memories integrated with telecom-band systems for scalable quantum networking applications.