The observation of superconductivity in infinite-layer nickelates provides an appealing new platform to explore a superconducting mechanism. Rationalizing the ground state magnetic order and spin dynamics in undoped compounds are the foundation for understanding the superconducting mechanism. Here, magnetic properties of infinite-layer LaNiO2 are investigated and compared with cuprate analog CaCuO2 by combining first-principles and spin-wave theory calculations. We reveal that LaNiO2 exhibits quasi-two-dimensional (2D) antiferromagnetic (AFM) order that mimics that of cuprate superconductors. Moreover, the electronic origin of the quasi-2D AFM state and the simulated dispersion of magnetic excitations in LaNiO2 show strong resemblance to that of NdNiO2. The establishment of a direct connection with the cuprates from the electron, orbital, and spin degrees of freedom provides solid theoretical basis to elucidate the origin of superconductivity in infinite-layer nickelates.