Lawn mowers, string trimmers and other lawn-care equipment can damage a tree bark's cambium layer, which is important in conducting water and nutrients up the trunk. Once this tissue is damaged, it remains that way, as there is no treatment for the damage.
Cut the sod in a circle around the tree, 4 feet away from the trunk. This gives you plenty of room for mowing and weeding without putting the tree in jeopardy.
A 2-inch-thick layer of mulch around the base of the tree, 6 inches away from it, keeps down weeds. If you decide not to use mulch, you will need to hand pull any weeds that sprout between the sod and the tree.