Traditional optical fibers are insensitive to magnetic fields, however many applications would benefit from fiber-based magnetometry devices. In this work, we demonstrate a magnetically sensitive optical fiber by doping nanodiamonds containing nitrogen vacancy centers into tellurite glass fibers. The fabrication process provides a robust and isolated sensing platform as the magnetic sensors are fixed in the tellurite glass matrix. Using optically detected magnetic resonance from the doped nanodiamonds, we demonstrate detection of local magnetic fields via side excitation and longitudinal collection. This is a first step towards intrinsically magneto-sensitive fiber devices with future applications in medical magneto-endoscopy and remote mineral exploration sensing.