Vladimir Putin, Russia's prime minister, announced the ban at a cabinet meeting on Thursday, saying it was necessary even though the country has sufficient reserves.
"We need to prevent a rise in domestic food prices, we need to preserve the number of cattle and build up reserves for the next year," he said during the televised meeting.
The majority of the damage to Russia's wheat crop has been caused by the drought - one of the worst in decades - as much of the country suffers through the hottest summer since record-keeping began 130 years ago.
Wildfires raging through much of western Russia have spread into farmland and there are fears that more fields will be lost.
Following the announcement of the ban, Egypt, the world's largest wheat importer, said it hoped that Russia would honour existing wheat contracts.
"If a decision is issued and it is an official decision the Russian government has to ... allow [buyers] to implement the contracts that have been completed, then ban any other contracts after August 15," said Nomani Nomani, the chairman of Egypt's General Authority for Supply Commodities (Gasc).
"The Russian government has the right to take any decision that suits it."
Gasc has signed contracts for the purchase of 540,000 tonnes of wheat from Russia for delivery between August 1 and September 10.