Roundup, which uses the active ingredient glyphosate, works as a non-selective herbicide, killing nearly any plant it touches. The leaves absorb the chemical and transmit it through the plant's vascular system, spreading the poison and killing the plant. It's typically administered as a spray, which is where the danger lies: the wind can carry spray to plants you don't want to hurt, such as your grapevines.
The tiny droplets created when you spray Roundup on your weeds are light enough for the wind to easily transport. The herbicide can travel up to half a mile on windy days, according to the Oregon State University Extension Service. When the droplets touch your grapevine leaves, they cause damage. A few drops might leave nothing more than scattered brown or yellow spots, but too much herbicide absorbed by the leaves can travel throughout the vine and cause dieback or death. To help prevent drift, choose a day that's not windy or when the wind is less than 5 mph.
The woody stem of grapevines isn't harmed by Roundup; the vulnerable parts are the leaves and new, green vines. The only danger with the main stem is if it has open wounds, such as if you've recently trimmed away suckers. Wrapping plastic around the base or blocking it with a large piece of cardboard can help prevent damage through open wounds when you're spraying weeds directly under the vine.
Because the leaves and new vines drink in the herbicide, always protect your vine when you're spraying Roundup in your yard. Drape clear plastic over the vine temporarily, then remove it when you're finished spraying. Spraying in the fall is more likely to cause damage because the vine is actively storing nutrients for the cold months, so spray for weeds when the vine is dormant or early in the growing season.