InternationalSpeaking in an interview with the business daily Kommersant, Peskov said that he initially had only a small fever and was undergoing treatment at home.
He said he was hospitalised after he had a computer tomography that showed both of his lungs were affected.
The 52-year-old Peskov said Monday that he contracted the virus but didn't give details of his condition.
He is the fourth senior Russian official to test positive for the virus. Prime Minister Mikhail Mishustin announced that he was infected on April 30, and in the following days Construction Minister Vladimir Yakushev and Culture Minister Olga Lyubimova also tested positive.
It wasn't clear when those officials last met with President Vladimir Putin, who has limited his public appearances and held most of his meetings online.
Russia has ranked second after the United States in the number of infections, with over 242,000 cases, including 2,212 deaths. (AP) INDIND