The pile foundation construction adjacent to an operational subway tunnel can induce the creep effects of the surrounding soil of the tunnel, resulting in the deformation of the existing tunnel lining and potentially compromising the safe operation of the tunnel. Therefore, the Mindlin solution and the generalized Kelvin viscoelasticity constitutive model were employed to establish the theoretical calculation model for the deformation of the adjacent subway tunnel caused by the pile construction. Then, the effect of pile construction on the deformation of adjacent tunnels under different pile-tunnel spacing was analyzed via three-dimensional numerical simulation and theoretical calculation methods and compared with the field monitoring data. The results showed that the theoretical and numerical data are in agreement with the field monitoring data. The theoretical model provides closer predictions to the field-measured values than the numerical simulation. As the distance between the pile and the tunnel increases, both the vertical settlement and the horizontal displacement of the subway tunnel lining exhibit a gradual reduction. In the hard plastic clay region of Hefei City (China), pile foundation construction near an operational subway tunnel can be classified into three distinct zones based on proximity to the tunnel: the high-impact zone (3.0 D). The pile foundation in high-, moderate-, and low-impact zones should be monitored for 7 days, 3 days, and 1 day, respectively, to ensure the stable deformation of the lining.