The actress added: "Fever and fatigue are my main symptoms. Take care of yourself and do take this seriously!"
Kurylenko starred opposite Daniel Craig in "Quantum of Solace" as Bolivian secret agent Camille Montes, a role for which she did dialect training.
"The Death Of Stalin" actress, who was born in the Soviet-era Ukraine but is now a French citizen, wrote her Instagram caption in both English and the Cyrillic alphabet.
Russian reports say she has lived in London for around a decade, but she did not say where she is undergoing quarantine.
She said: "To bring down the temperature, they said to take Paracetamol, which I do. That's all. Nothing more to do. Of course, I still take vitamins for myself like that. And I eat garlic, just for the immune system. I drink water. Squeeze lemons in water. That's all."
Take a look at her post below:
Kurylenko's diagnosis comes days after Hollywood star Tom Hanks and his wife Rita Wilson became the first major Hollywood celebrities to contract the virus.
Kurylenko had recently finished shooting her upcoming movie "The Bay Of Silence", according to The Hollywood Reporter. It is not yet clear if anyone else will need to be quarantined as a result of her testing.
She has a number of releases in the offing, including a French Netflix movie called "Sentinelle" that is in post-production and due out this August. She is also slated to appear in a Chinese action thriller called "The Hunting", originally called "Fox Hunt".