Lara Manton, who along with her father, Tony, and her brother, Chris, runs Beekeeper Honey, in Brackley, said the hives were only accessible across a field.
She believes the thieves would have required a substantial vehicle, such as a 4x4 and a trailer, to move them.
The hives, which weigh 20kg each, were overwintering on the site and were believed to have been taken sometime between February 17 and 24.
Speaking to the Bicester Review, Miss Manton said: “We are really sad. The biggest worry is not the monetary value but the person who has taken them has to look after them and make sure they don’t swarm or starve. The common misconception is you can put a hive in your back garden and leave it, but the bees do need care and attention.”
She added come May or June, if the bees start to swarm, the hives would become a ‘nightmare’ for whoever had taken them.
“We hope to get the bees back and make people realise taking hives is not a clever thing to do,” she said.
“All of the beekeeping community has rallied round us – it has been fantastic. It is heartwarming that everyone has been so caring. We’ve had bee farmers offer to lend us some of their hives.”
The hives are painted in bright colours such as green and orange and Miss Manton urged the public to look out for anything unusual such as multiple hives suddenly appearing in a field.
“It is my first proper year with my own hives. I did my beekeeping apprenticeship and I am graduating this year,” she said.
“If I hadn’t been working for my family’s business then my whole business could be almost shut down from the theft. To be part of the Bee Farmers Association, you have to have 40 hives or above so 40 hives could be your whole business.”
Thames Valley Police are appealing for witnesses or anyone with any information to contact them on 101.
Miss Manton said: “You don’t want to have worries about hives being stolen. It is a hard enough job as it is without the thought of another thing adding to the difficulty of it.
“It is a big deal for us – it is something we care about and are passionate about.”