"A tribute to the famed valour of Russia's soldiers. PM @narendramodi lays wreath at the Tomb of the Unknown Soldier," external affairs ministry spokesman Vikas Swarup tweeted.
The Tomb of the Unknown Soldier is a war memorial dedicated to the Soviet soldiers killed in World War II and is located by the Kremlin wall in the Alexandrovsky Garden.
In December 1966, on the 25th anniversary of the 1941 Battle of Moscow, the remains of the unknown soldiers killed were moved from the 41st kilometre on the Leningrad highway to the Alexandrovsky garden.
On May 8, 1967, the memorial architectural ensemble of the Tomb of the Unknown Soldier was unveiled to the public.
The eternal flame of glory that comes from the centre of a bronze military star was lit from the flame that burns on the Field of Mars in St. Petersburg.
"Your name is unknown, your deeds are immortal," is inscribed on the granite slab of the gravestone.
Earlier in the day, Modi visited Russia's National Crisis Management Centre (NCMC), also known as EMERCOM, in Moscow and was given a rundown on how its works.
Modi, who arrived in Moscow on Wednesday and was hosted for a private dinner by Russian President Vladimir Putin, will attend the 16th India-Russia annual summit meeting later on Thursday.
A raft of agreements spanning a broad spectrum of sectors are expected to be signed following the summit-level talks with trade being a major focus area.
Modi and Putin are scheduled to meet a delegation of Indian and Russian CEOs in the Kremlin.
Modi will address a gathering of Friends of India and also meet members of the Indian community in Russia.