Distributed multichannel active noise control (DMCANC) offers effective noise reduction across large spatial areas by distributing the computational load of centralized control to multiple low-cost nodes. Conventional DMCANC methods, however, typically assume synchronous communication and require frequent data exchange, resulting in high communication overhead. To enhance efficiency and adaptability, this work proposes an asynchronous communication strategy where each node executes a weight-constrained filtered-x LMS (WCFxLMS) algorithm and independently requests communication only when its local noise reduction performance degrades. Upon request, other nodes transmit the weight difference between their local control filter and the center point in WCFxLMS, which are then integrated to update both the control filter and the center point. This design enables nodes to operate asynchronously while preserving cooperative behavior. Simulation results demonstrate that the proposed asynchronous communication DMCANC (ACDMCANC) system maintains effective noise reduction with significantly reduced communication load, offering improved scalability for heterogeneous networks.