A connected graph \(G\) is called \(l_1\)-embeddable, if \(G\) can be isometrically embedded into the \(i\)-space. The hexagonal Möbius graphs \(H_{2m,2k}\) and \(H_{2m+1,2k+1}\) are two classes of hexagonal tilings of a Möbius strip. The regular quadrilateral Möbius graph \(Q_{p,q}\) is a quadrilateral tiling of a Möbius strip. In this note, we show that among these three classes of graphs only \(H_{2,2}\), \(H_{3,3}\), and \(Q_{2,2}\) are \(l_1\)-embeddable.