It was shown in [Colloq. Math. 131(2), 219–231 (2013)] that one can extend the domain of Fourier transform of a commutative hypergroup K to Lp(K) for 1 ≤ p≤ 2 , and the Hausdorff–Young inequality holds true for these cases. In this article, we examine the structure of non-zero functions in Lp(K) for which equality is attained in the Hausdorff–Young inequality, for 1 < p< 2 , and further provide a characterization for the basic uncertainty principle for commutative hypergroups with non-trivial center.