This paper proposes a novel method for aligning multiple genomic or proteomic sequences using a fuzzyfied Hidden Markov Model (HMM). HMMs are known to provide compelling performance among multiple sequence alignment (MSA) algorithms, yet their stochastic nature does not help them cope with the existing dependence among the sequence elements. Fuzzy HMMs are a novel type of HMMs based on fuzzy sets and fuzzy integrals which generalizes the classical stochastic HMM, by relaxing its independence assumptions. In this paper, the fuzzy HMM model for MSA is mathematically defined. New fuzzy algorithms are described for building and training fuzzy HMMs, as well as for their use in aligning multiple sequences. Fuzzy HMMs can also increase the model capability of aligning multiple sequences mainly in terms of computation time. Modeling the multiple sequence alignment procedure with fuzzy HMMs can yield a robust and time-effective solution that can be widely used in bioinformatics in various applications, such as protein classification, phylogenetic analysis and gene prediction, among others.