We propose a finite-alphabet symbol-level precoding technique for massive multiuser multiple-input multiple-output (MU-MIMO) downlink systems which are equipped with finite-resolution digital-to-analog converters (DACs) of any precision. Using the idea of constructive interference (CI), we adopt a max-min fair design criterion which aims to maximize the minimum instantaneous received signal-to-noise ratio (SNR) among the user equipments (UEs) while ensuring a CI constraint for each UE under the restriction that the output of the precoder is a vector with finite-alphabet discrete elements. Due to this latter constraint, the design problem is an NP-hard quadratic program with discrete variables, and hence, is difficult to solve. In this paper, we tackle this difficulty by reformulating the problem in several steps into an equivalent continuous-domain biconvex form, including equivalent representations for discrete and binary constraints. Our final biconvex reformulation is obtained via an exact penalty approach and can efficiently be solved using a standard cyclic block coordinate descent algorithm. We evaluate the performance of the proposed finite-alphabet precoding design for DACs with different resolutions, where it is shown that employing low-resolution DACs can lead to higher power efficiencies. In particular, we focus on a setup with one-bit DACs and show through simulation results that compared to the existing schemes, the proposed design can achieve SNR gains of up to 2 dB. We further provide analytic and numerical analyses of complexity and show that our proposed algorithm is computationally efficient as it typically needs only a few tens of iterations to converge.