The low temperature magnetoresistance of graphene functionalized by an array of magnetic Terbium Phthalocyanines molecules is found to exhibit a magnetic field-dependent 1/f noise, along with universal conductance fluctuations (UCFs) typical of a mesoscopic phase-coherent sample. A thorough analysis of the magnetic field, temperature and chemical potential dependence of this 1/f noise and UCFs reveals that 2D Ising spin-glass like, magnetic correlations whose correlation time and length scales increase at low temperature, are induced in graphene through exchange interactions between the magnetic molecules and charge carriers in graphene. These experiments show that graphene functionalized with organic molecules constitutes a versatile platform for the investigation of magnetic phase transitions in two dimensions.