Singh travelled by an Indian Air Force aircraft, while strictly following all laid precautions against the coronavirus infection, officials said.
The last foreign trip abroad by a senior member of the union cabinet was by Finance Minister Nirmala Sitharaman
when she visited Riyadh from Feb 22-24 to attend a meeting of G-20 finance ministers. Days before Sitharaman's trip, External Affairs Minister S Jaishankar visited Germany from February 18 to 19.
The defence minister's visit to Russia comes in the midst of the escalating border standoff between India and China, particularly after the killing of 20 Indian Army personnel by Chinese troops in eastern Ladakh's Galwan Valley on June 15.
Russia has been in touch with both India and China following their border row and officials did not rule out discussion on the matter during Singh's meetings in Moscow.
"Leaving for Moscow on a three-day visit. The visit to Russia will give me an opportunity to hold talks on ways to further deepen the India-Russia defence and strategic partnership. I shall also be attending the 75th Victory Day Parade in Moscow," Singh tweeted before leaving for Moscow.
Officials said Singh went ahead with the visit, notwithstanding the border row with China, due to India's decades-old military ties with Russia.
They said the defence minister in his talks with top Russian military brass is expected to request for the timely delivery of the S-400 missile systems.
Russian Deputy Chief of Mission Roman Babushkin recetly told PTI that there could be some delays in implementation of military contracts including the S-400 one in view of the coronavirus pandemic.
In October 2018, India had signed a $ 5 billion deal with Russia to buy five units of the S-400 air defence missile systems, notwithstanding warning from the Trump administration that going ahead with the contract may invite US sanctions.
Last year, India made the first tranche of payment of around $ 800 million to Russia for the missile systems. Moscow was to begin the delivery of the system by second half of next year.
The defence minister is also expected to request Moscow to cut delays in supply of spares of key Russian-origin platforms like tanks, fighter jets and helicopters.
Russia has been one of India's key suppliers of arms and ammunition. However, it has been a long-standing grievance of armed forces that supply of critical spares and equipment from Russia takes a long time affecting maintenance of military systems procured from that country.
A tri-service 75-member Indian military contingent has already reached Moscow to participate in the parade. The Indian team will participate in the parade alongside armed forces personnel from at least 11 countries including China.
"The visit of the defence minister will strengthen the longstanding special and privileged strategic partnership between India and Russia," the defence ministry said on Saturday.
"The Indian participation in the victory day parade will be a mark of tribute to the great sacrifices made by Russia and other nations in the Second World War in which Indian soldiers also participated and made supreme sacrifice," it said.