Serbian doctors say two people were seriously injured and up to 300 have sought medical help after Hungarian police used the tactics to stop migrants from entering the country.
"This kind of heavy-handed and aggressive response we are seeing on the Serbia-Hungarian border is not only appalling - it is unacceptable," said Gavin Crowden, World Vision UK's Head of Policy and Public Affairs.
He added that whilst a country has the "right and power to patrol its own borders" it "cannot be right that children who have walked for weeks on end to flee violence and bombs in Syria are being met with barbed wire and teargas in Europe".
Hungarian officials said some migrants had thrown missiles, including stones and bottles.
The charity, the first UK Christian aid agency to help refugees arriving in Europe, said it was continuing to give out urgent supplies at a camp in Horgos on the Serbia-Hungary border.
Gavin Crowden, from World Vision, said: "These children need safety and shelter. All countries - and European ones are no exception - have a duty to protect people fleeing conflict and persecution.
"This situation further underlines why a coherent European plan to address this refugee crisis - the worst since World War II - is urgently needed."
Joy Toose, World Vision's Rapid Response team member based in Serbia said: "There has been a growing sense of frustration in Horgos.
"In the past twenty-four hours, families have been arriving rapidly and they are getting more desperate than ever. Some are living in tents while others are out in the open.
"The situation is critical and World Vision is prioritising supporting families with children, but even so there are more people in need of food and water and we do not have the sufficient resources."
The charity has been supporting parents with "family packs" that contain basic items such as nappies, baby cream, wet wipes, a toy and sanitary pads for women.
