Antibiotic drug residues can adversely affect the human body. Lincomycin is a common veterinary drug that can form residues in foods of animal origin. However, the detection of trace residue levels of lincomycin residues in real samples is challenging. Here, a simple solid phase extraction (SPE) method was developed for the enrichment of lincomycin from cow milk samples before its detection by high-performance liquid chromatography-tandem mass spectrometry (HPLC-MS/MS). The adsorbent used in the SPE was a Cu-based metal-organic framework (Cu-MOF) prepared by the solvothermal synthesis approach. The prepared MOFs were characterized using scanning electron microscopy (SEM), Fourier-transform infrared spectroscopy (FT-IR), X-ray diffractometry (XRD), differential thermogravimetric analysis (TG-DTA), and N2 adsorption-desorption experiments. The adsorption capacity (adsorption equilibrium, extraction time, pH), and elution solvent parameters were investigated. Under the optimized conditions of the HPLC-MS/MS method, lincomycin was detected in the linear range of 10–200 g/L with a detection limit of 0.013 ng/mL. Commercial milk samples were spiked with lincomycin, and a recovery rate between 92.3% and 97.2% was achieved. Therefore, the current method can be successfully applied for the enrichment and determination of lincomycin from milk samples.