Shoygu, a longtime ally of the president, had been holding the post since 2012.
According to a decree published on the Kremlin's website, Putin appointed Shoygu as secretary of Russia's Security Council and recommended Andrei Belousov, a former deputy prime minister who specializes in economics, for his post.
Commenting on Putin's decision, Kremlin spokesman Dmitry Peskov said a civilian official will assume the post of head of the Ministry of Defense due to the need to introduce innovations in its work.
Belousov will also address the task of facilitating the integration of the defense economy into the country's economy.
The previous head of the Security Council, Nikolay Patrushev, has been appointed to a new position that will be announced in the coming days, Peskov said.
Other ministers responsible for various aspects of security as well as the foreign minister will be the same as in the previous Cabinet, he noted.
Russia's parliament will consider candidates for ministerial posts next week.
Comment: While this may be unrelated, Russia's Deputy Defence minister, allegedly friend of Shoigu's, was in court recently on corruption charges.