Physicians for Human Rights and the Israel and the Negev Coexistence Forum were among the groups, non-governmental organisations and villagers who lodged the appeal on Monday against the use of Roundup herbicide.
Israeli authorities have frequently used crop-dusting planes to destroy the harvest of beduin Arabs living in so-called "unrecognised" villages in Israel's southern Negev desert.
The statement said: "On seven different days in the last years at least 30,000 dunams (7,500 acres) of wheat, barley, and some vegetables have been sprayed in 12 villages. The crops are a part of the food consumed by the villagers and their livestock in the 'unrecognized' villages.
"The authorities ignored the simple instructions prohibiting aerial spraying, the exposures were produced without the notification or consent of the subjects, which, even if given, would still make the entire exercise unethical," said the statement, quoting the assessment of a leading epidemiologist, an expert in the spread of diseases.
Elihu Richter said the way the herbicide was being used was "a health risk to the residents and their animals, and can cause fertility problems, birth defects.
"There is even some evidence that this substance is cancerous," he said.
In the groups' petition to the court, it stated the Israeli Ministry of Health claim that: "According to the literature research that we conducted, Roundup is not poisonous to humans when it is used according to manufacturer's specifications."
However, the petition points out the manufacturer's directions state: "Do not apply this product using aerial spray equipment." The reason, the NGOs and other concerned groups point out, is the danger of spread of the chemical to adjacent residential areas and human exposure to it.
The herbicide poses health risks
to Palestinian livestock as well
In the warnings, the petition adds, it is cautioned that: "Regular caution must be used, as is used with any herbicides. Do not inhale, during spraying wear clothes that cover the entire body, keep livestock away from the sprayed area for seven days after spraying."
The spraying, the groups say, was done without any prior notice. "Part of the spraying was done in close proximity to people's residences."
In two cases, the petition adds: "People were in or near to the fields and were sprayed directly."
The beduins did not receive any information about the area where their fields were sprayed and no fences were erected to obstruct livestock from entering the area.
These people obtain their food "from these livestock and the harm caused to the livestock could bring about indirect harm to the people", the petition added.
"Part of the spraying was done in close proximity to people's residences ... in two cases people were in or near to the fields and were sprayed directly"
Rights groups petition
Many beduin, pastoral shepherds who have grazed their goats, sheep and camels on the same lands from generation to generation, now live in seven authorised settlement towns into which the Israeli authorities have tried to corral them since the 1970s.
But many reject what they call these "reservations", where unemployment is high. An increasing number have moved back to their old lands, living in around 40 unrecognised villages where they build homes without planning permission.