Multiple Sequences Alignment (MSA) of biological sequences is a fundamental problem in computational biology due to its critical significance in wide ranging applications including haplotype reconstruction, sequence homology, phylogenetic analysis, and prediction of evolutionary origins. The MSA problem is considered NP-hard and known heuristics for the problem do not scale well with increasing number of sequences. On the other hand, with the advent of new breed of fast sequencing techniques it is now possible to generate thousands of sequences very quickly. For rapid sequence analysis, it is therefore desirable to develop fast MSA algorithms that scale well with the increase in the dataset size. In this paper, we present a novel domain decomposition based technique to solve the MSA problem on multiprocessing platforms. The domain decomposition based technique, in addition to yielding better quality, gives enormous advantage in terms of execution time and memory requirements. The proposed strategy allows to decrease the time complexity of any known heuristic of O(N)^x complexity by a factor of O(1/p)^x, where N is the number of sequences, x depends on the underlying heuristic approach, and p is the number of processing nodes. In particular, we propose a highly scalable algorithm, Sample-Align-D, for aligning biological sequences using Muscle system as the underlying heuristic. The proposed algorithm has been implemented on a cluster of workstations using MPI library. Experimental results for different problem sizes are analyzed in terms of quality of alignment, execution time and speed-up.