The regulator said its decision is due to the outbreak of coronavirus – the auction was scheduled to take place in April.
France is the last major economy in Europe not to have allocated spectrum for 5G.
An spokesperson from Arcep said the frequency sale will go ahead later in the year, once there is more information about the evolution of the virus outbreak.
The French President, Emmanuel Macron, imposed a lockdown on the French population from Tuesday this week for at least 14 days in an effort to contain the virus.
When details of the auction were announced last November, Arcep said that it would award 310 MHz of frequencies in the 3.4-3.8 GHz band in four blocks of 50 MHz with the remainder in blocks of 10 MHz.
The French government previously said it aims to raise at least 2.17 billion euros ($2.38 billion) from the spectrum sale.
The country’s four operators – Orange, SFR, Iliad and Bouygues – are all expected to take part in the 5G auction.