Most vegetables suffer some transplant shock in the first days after planting them out to their permanent bed. The leaves droop and flower buds my drop off from the plant. Transplanting damages some of the smaller roots on the vegetables an it takes two or more days for the remaining roots to establish enough to begin sending adequate supplies of moisture and nutrients to the leaves. Most plants quickly recover and stop drooping. Growing transplants in plantable pots, such as peat pots, allows you to transplant the vegetables without disturbing the roots, which minimizes transplant shock.
The plants may wilt if they aren't properly hardened-off and adjusted to the climate outdoors. Transplants can't experience the heat, sunlight and wind that is present outdoors when they are still growing inside. They may droop until they adjust to the outdoor conditions. Leaving the plants in their pots for a week or two before transplanting, but setting them outside in a protected area, hardens them to outdoor conditions. Hardened plants suffer less shock after transplanting and bounce back from any wilt more quickly.
All plants lose moisture through their leaves. Heat, sun and wind speeds the moisture loss and makes the vegetables more likely to wilt. Try and transplant on an overcast but still day so the plants can establish before suffering from the rapid moisture loss. If you must plant in sunny weather, do so in late afternoon after the heat of the day has passed. Vegetable transplants already suffering from droop after transplanting usually perk up within a few days if the soil remains moist but not soggy.
Hard, compacted soils or a sandy dry bed can cause plants to wilt from water stress. Both too much and too little moisture stresses the transplants. Plants that prefer cooler temperatures, such as lettuce, droop in hot, full sun beds. Providing enough moisture and mulching the soil to keep the roots cool may prevent wilting. Full-sun, warm-temperature plants, such as tomatoes, may wilt after transplanting if there is cool weather. The plants bounce back once temperatures warm. If temperatures drop below freezing after transplanting, cover the warm-weather vegetables with a hot cap, blanket or other frost protection device.