Data clustering is useful in a wide range of application areas. The Animal Migration Optimization (AMO) algorithm is one of the recently introduced swarm-based algorithms, which has demonstrated good performances for solving numeric optimization problems. In this paper, we presented a modified AMO algorithm with an entropy-based heuristic strategy for data clustering. The main contribution is that we calculate the information entropy of each attribute for a given data set and propose an adaptive strategy that can automatically balance convergence speed and global search efforts according to its entropy in both migration and updating steps. A series of well-known benchmark clustering problems are employed to evaluate the performance of our approach. We compare experimental results with k-means, Artificial Bee Colony (ABC), AMO, and the state-of-the-art algorithms for clustering and show that the proposed AMO algorithm generally performs better than the compared algorithms on the considered clustering problems.