Among the newly observed structures in the heavy-quarkonium mass region, some have been proposed to be hadronic molecules. We investigate the consequences of heavy-quark flavor symmetry on these heavy meson hadronic molecules. The symmetry allows us to predict new hadronic molecules on one hand, and test the hadronic molecular assumption of the observed structures on the other hand. We explore the consequences of the flavor symmetry assuming the X(3872) and Zb(10 610) as an isoscalar DD̅ * and isovector BB̅ * hadronic molecule, respectively. A series of hadronic molecules composed of heavy mesons are predicted. In particular, there is an isoscalar 1++ BB̅ * bound state with a mass about 10 580 MeV which may be searched for in the Υ(1S,2S)π+π-π0 mass distribution; the isovector charmonium partners of the Zb(10 610) and the Zb(10 650) are also predicted, which probably corresponds to the very recently observed Zc(3900) and Zc(4025) resonances by the BESIII Collaboration.