Ternary semihyperring is an algebraic structure with one binary hyper operation and ternary multiplication. In this paper, we give some properties of hyperideals in ternary semihyperring. We introduce the notion of simple, (0-)simple ternary semihyperring and characterize the minimality and maximality of hyperideals in ternary semihyperring. The relationship between them is investigated in ternary semihyperring extending and generalizing the analogous results for ternary semirings.