The magnetic dipole and the electric quadrupole hyperfine splitting in heavy Li-like ions is calculated for the (1s)²2p_1/2 and (1s)²2p_3/2 states. The numerical results include the one-electron contributions as well as the interelectronic-interaction correction of order 1/Z, calculated within a rigorous QED approach. Total hyperfine splitting energies are presented for heavy Li-like ions in the range Z = 49-83.