We study by first-principles calculations a densely packed island of organic molecules (F_{4}TCNQ) adsorbed on graphene. We find that with electron doping the island naturally forms a p-n junction in the graphene sheet. For example, a doping level of ∼3×10^{13} electrons per cm^{2} results in a p-n junction with an 800 meV electrostatic potential barrier. Unlike in a conventional p-n junction in graphene, in the case of the junction formed by an adsorbed organic molecular island we expect that the Klein tunneling is inhibited, even without an applied external magnetic field. Here Klein tunneling is inhibited by the ferromagnetic order that spontaneously occurs in the molecular island upon doping. We estimate that the magnetic barrier in the graphene sheet is around 10 mT.