Stir together first 7 ingredients in a 13- x 9-inch baking dish; set aside.
Cut eggplant into 1-inch cubes. Cut bell peppers into 1 1/2-inch pieces. Cut onion into 8 wedges. Cut zucchini and yellow squash into 1/2-inch-thick slices.
Thread vegetables onto 6 (10-inch) skewers; place in sauce mixture, turning to coat. Cover and let stand 1 hour.
Remove kabobs from marinade, reserving marinade.
Grill, covered with grill lid, over medium heat (300° to 350°) 12 to 17 minutes; turn occasionally and baste with reserved marinade.
