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The migration of photoinitiators (PIs): benzophenone (BP), ethyl 4-dimethylaminobenzoate (EDAB), and 4-chlorobenzophenone (CBP), from polyethylene (PE)-coated paper to 4% (v/v) acetic acid and 10% (v/v) salt-simulated food solution was quantitatively analyzed using gas chromatography–mass spectrometry. The migration behavior of the three PIs was studied under three specific working conditions: conventional heating, microwave power, and random vibration level. The migration rate of the three PIs in acidic food simulants was ranked from BP > EDAB > CBP under the specific working conditions. The mobility of the three PIs increased with increasing temperature, microwave power, and random vibration acceleration in 4% (v/v) acetic acid by 10, 10, and 15%, respectively. The experimental migration data of three PIs in PE-coated paper under different temperatures and microwave powers were used to establish the Crank monolayer migration model according to Fick’s second law. The diffusion coefficient D increased with an increase in experimental conditions. According to the migration data under the condition of random vibration level, a mathematical model conforming to the Fick model was established, fitting the migration process. These results showed that conventional heating, microwave heating, and vibration could affect the food safety of PE-coated paper.