The video clip, entitled Winnie Pooh and the Bees, showed a group of teenage girls dancing on stage in stripy leotards, long socks and mini-skirts,
They perform hip-thrusting moves characteristic of twerking.
The Youtube video clip spread fast online, sparking controversy.
Some commentators labelled it "pornographic", and some called for those who staged it to be sacked or even prosecuted.
Others were disturbed that the girls' outfits were orange and black - the colours of the St George ribbon that has become a symbol of patriotism in Russia.
The striped ribbon was primarily associated with the Soviet victory in World War Two, but is now used by pro-Russian fighters in eastern Ukraine.
The decision to close the dance studio pending an investigation was taken after an emergency meeting at the local mayor's office in the city in the Urals, according to the official government newspaper Rossiskaya Gazeta.
The head of the school,  known as Credo, was called in as were parents of the dancers and the director of the state-run House of Culture where the "scandalous" dance was performed.
The school said the twerking class had already been cancelled and the girls would study classical choreography and hip-hop instead.
But the mayor's office chose to cancel all classes until the enquiry is over. The school's website has also been disabled.
The local Orenburg branch of Russia's powerful Investigative Committee described the dancers as "under age" and wearing "revealing costumes". It said it would look into the exact age of participants and investigate those in charge of the dance school and their paperwork.
Earlier, Russia's Interfax news agency reported that the committee was investigating whether the performance amounts to negligence or even "debauched action", which is punishable by a range of sanctions from community service to three years behind bars.
The head of the dance school is quoted by Moskovsky Komsomolets newspaper saying that the parents all knew what their children were doing and gave their written permission.
Officials in the Russian town of Orenburg have closed down a dance school after a performance of teenage girls "twerking" caused a sensation - and consternation - on the internet.