Monopolistic competition creates a DWL because firms have market power.
Like a monopoly, firms in monopolistic competition have market power. That is, they are price searchers or price makers. Because they have a differentiated product, they are able to set price above marginal cost. By definition, this is deadweight loss. Like a monopoly, firms in monopolistic competition produce a quantity that is too low and at a price that is too high (compared to perfect competition).
Two qualifications are needed. First, the concept of DWL is a bit misleading, particularly in the context of market structures. Comparing monopolistic competition (or monopoly) to perfect competition is meaningless. Second, economists usually don’t worry much about the DWL of monopolistic competition. We are more interested in the excess capacity generated by monopolistically competitive firms in long run equilibrium.