Advance oxidation processes (AOPs) based on periodate (PI) offer new methods for removing pollutants, but the activation of PI by carbon nanotubes and its composites has been rarely reported. In this study, N-doped carbon nanotubes encapsulated cobalt (Co@NCNTs) was synthesized through melamine assisted ZIF–67 pyrolysis, and it was used to activate PI for the tetracycline (TC) degradation. Effects of experimental parameters including catalyst dosage, periodate concentration, initial pH, and temperature were investigated. The results show that this system exhibited excellent activation performance under wide pH (4–10) with a low reaction activation energy (Ea = 8.874 kJ/mol). Radical quenching experiments manifested that iodate radical (IO3) played a main role in the TC elimination, followed by superoxide radical (O2−), singlet oxygen (1O2), and hydroxyl radicals (OH). Additionally, it is found that IO4− is not converted into toxic iodine species (I2, HOI) but nontoxic iodate (IO3−), indicating that no secondary pollution occurred. Finally, possible TC degradation pathways were proposed based on the results of high-performance liquid chromatography mass spectrometry (HPLC-MS) analysis. This article provides a novel approach for the activation PI to remove pollutants and a theoretical support for practical applications.