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Although traditional optical fibers are not sensitive to magnetic fields, many applications would benefit from fiber-based magnetometry devices. In this study, a magnetically sensitive optical fiber was demonstrated using 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, detection of local magnetic fields via side excitation and longitudinal collection were demonstrated. This is an important step towards intrinsically magneto-sensitive fiber devices with future applications in medical magneto-endoscopy and remote mineral exploration sensing.