Hydroponic vegetables are not necessarily organic, and, thus far, the USDA's National Organic Program has not made that determination as to whether hydroponic grows can meet organic requirements. Since that term has a very precise meaning and the USDA regulates the use of the term for food products, it is reasonable to assume that hydroponic farms may not be able to meet the NOP qualifications. According to NOP, an organic plant product must be grown without the use of:
Genetically Modified Organisms (GMOs)
Further, any organic product must emphasize the use of renewable resources during production.
To earn an “organic” label, an inspector must certify the farm as meeting these requirements. Because the NOP hasn't weighed in on the issue, some inspectors (known officially as Accredited Certifying Agents or ACAs for short) have gone ahead and issued organic certifications to some hydroponic farms. When the NOP sets its official stance on whether hydroponic operations can be organic, those certifications could be canceled.
Just remember, a food product is not officially organic without that USDA seal!