"An attempt by the Kyiv regime to attack a zone where civil infrastructure is located, including an airport that receives international flights, is a new terrorist act," foreign ministry spokeswoman Maria Zakharova said on Telegram.
The Russian military said it had downed all five drones, and that there was no damage or casualties.
Four drones were destroyed by anti-air defence systems while a fifth was neutralised by "electronic means" before crashing, it said.
Emergency services cited by the RIA Novosti news agency said one of the drones was neutralised at Kubinka, about 40 kilometres (25 miles) from Vnukovo, whose functioning was briefly interrupted by the attack.
Several flights were redirected to other airports and Russia's air transport agency said traffic at Vnukovo resumed at 0500 GMT.