Let M be a σ-finite von Neumann algebra, equipped with a normal faithful state ϕ, and let A be maximal subdiagonal subalgebra of M. We prove a Beurling-Blecher-Labuschagne theorem for A-invariant subspaces of Lp(A) when 1 ≤ p < ∞. As application, we give a characterization of outer operators in Haagerup noncommutative Hp-spaces associated with A.