Modular quantum architectures have emerged as a promising solution for scalable quantum computing systems. Executing circuits in such distributed systems necessitates non-local operations between modules, incurring significant communication overhead. In this work, an optimized quantum circuit mapping technique called DQTetris is proposed to reduce inter-module communications. DQTetris employs a hierarchical framework that first seeks a global communication-free qubit mapping assignment under module capacity constraints. If infeasible, it searches for subcircuits with local communication-free qubit assignments via layer-wise gate pruning. Executing adjacent subcircuits with different qubit assignments incurs inter-module data teleportation. DQTetris minimizes these overheads by reducing qubit reassignment events through optimal circuit segmentation, qubit assignment selection, and adaptive gate teleportation. Experiments show that compared with existing methods, DQTetris can achieve average reductions in communication costs ranging from 28% to 75% across various benchmarks.