51V NMR studies on CaV₂O₄ single crystals and 17O NMR studies on 17O-enriched powder samples are reported. The temperature dependences of the 17O NMR linewidth and nuclear spin-lattice relaxation rate give strong evidence for a long-range antiferromagnetic transition at T_N=78 K in the powder. Magnetic susceptibility measurements show that T_N=69 K in the crystals. A zero-field 51V NMR signal was observed at low temperatures (f≈237 MHz at 4.2 K) in the crystals. The field-swept spectra with the field in different directions suggest the presence of two antiferromagnetic substructures. Each substructure is collinear, with the easy axes of the two substructures separated by an angle of 19(1)°, and with their average direction pointing approximately along the b axis of the crystal structure. The two spin substructures contain equal numbers of spins. The temperature dependence of the ordered moment, measured up to 45 K, shows the presence of an energy gap E_G in the antiferromagnetic spin wave excitation spectrum. Antiferromagnetic spin wave theory suggests that E_G∕k_B lies between 64 and 98 K.