A jury has ordered Monsanto Co. to pay $289.2 million in a landmark lawsuit over whether exposure to two of its powerful weed killers caused cancer.

The jury verdict, in San Francisco Superior Court, is the latest setback for Monsanto, now part ofBayer AG, as its flagship weed killer Roundup comes under increased scrutiny following the 2015 determination from the World Health Organization that glyphosate, the active ingredient in Roundup herbicides, is probably carcinogenic.

On...