Let φ : R n × [ 0 , ∞ ) → [ 0 , ∞ ) satisfy that φ ( x , ⋅ ) , for any given x ∈ R n , is an Orlicz function and that φ ( ⋅ , t ) is a Muckenhoupt A ∞ weight uniformly in t ∈ ( 0 , ∞ ) . The weak Musielak–Orlicz Hardy space WH φ ( R n ) is defined to be the set of all tempered distributions such that their grand maximal functions belong to the weak Musielak–Orlicz space WL φ ( R n ) . For parameter ρ ∈ ( 0 , ∞ ) and measurable function f on R n , the parametric Marcinkiewicz integral μ Ω ρ related to the Littlewood–Paley g -function is defined by setting, for all x ∈ R n , μ Ω ρ ( f ) ( x ) : = ( ∫ 0 ∞ | ∫ | x − y | ≤ t Ω ( x − y ) | x − y | n − ρ f ( y ) d y | 2 d t t 2 ρ + 1 ) 1 / 2 , where Ω is homogeneous of degree zero satisfying the cancellation condition. In this article, we discuss the boundedness of the parametric Marcinkiewicz integral μ Ω ρ with rough kernel from weak Musielak–Orlicz Hardy space WH φ ( R n ) to weak Musielak–Orlicz space WL φ ( R n ) . These results are new even for the classical weighted weak Hardy space of Quek and Yang, and probably new for the classical weak Hardy space of Fefferman and Soria.