Machine (10) and method for treating containers (12) of liquids comprising a loading station (15) into which baskets (23) are loaded containing, according to a desired pattern of disposition, the containers (12) to be subjected to washing, a filling station (18) in which the washed containers (12) are filled with new liquid, and a re-closing station (19) in which the containers (12) are closed by the relative lids (11). The re-closing station (19) comprises a closing device (63) provided with gripper members (70) by means of which the lids (11) are picked up and positioned so as to close the containers (12), and loading members (66) that automatically direct the lids (11) toward the closing device (63) in a manner consistent with the desired pattern of disposition of the containers (12) in the baskets (23). The closing device (63) comprises movement members (69) that move the gripper members (70) automatically between a pick-up position in correspondence with the loading members (66) and a position of closure in correspondence with the containers (12). The loading members (66) comprise stop elements (67), able to be selectively activated to automatically dispose the lids (11) in a manner consistent with the predetermined pattern of disposition of the containers (12).