He is due to begin his visit by laying a wreath at the Grave of an Unknown Soldier near the Kremlin wall, before talks with Mr Medvedev.
The Russian president said in an interview for Italian media released on Sunday that US missile shield plans for Europe put a "very prominent nuclear country like Russia... in a difficult situation".
Arms control will top the agenda of the summit. The Soviet-era Start I accord expires in December.
The White House co-ordinator for weapons of mass destruction, Gary Samore, ruled out any final agreement on renewing Start being reached this week, but he did see an "announcement" being made.
"I think you will see an announcement that indicates some progress toward reaching that objective," he told reporters.
On Afghanistan, the US is confident of obtaining Moscow's approval for flying troops and weapons through Russian airspace.
President Obama will also meet Russian journalists and civil society activists.
A University of Maryland opinion poll released on Sunday suggests that 75% of Russians believe the US abuses its greater power and only 2% have "a lot of confidence" that Mr Obama will do the right thing in world affairs.
START I TREATY
Strategic Arms Reduction Treaty (Start I), signed in July 1991, cut the numbers of nuclear warheads by roughly half to 6,000. It expires on 5 December 2009
Start II, signed in 1993, was intended to further reduce number of warheads and ban use of Multiple Independently Targetable Re-entry Vehicle (MIRV) warheads, but was never ratified
In 2002, Sort, better known as the Treaty of Moscow, committed both sides to cut arsenals by two-thirds to 1,700-2,200 deployed warheads
Neither of Russia's main TV news bulletins on Sunday evening led with the impending US visit.
"This is being played as essentially a low-key visit that shows the American leadership's respect for the Russian leadership," Dmitry Trenin, head of the Moscow Carnegie Centre think-tank, told Reuters news agency.
"This is not some star coming to town."
Nonetheless, correspondents say Mr Obama can expect a smoother reception than he received on a 2005 visit to Russia when he and other visiting US Congressmen were detained for three hours at an airport in the Urals city of Perm.
They were kept in an "uncomfortably stuffy room adjacent to the tarmac", a US spokesman said, as they resisted Russian customs officials' demands to search their plane.
Mr Obama later brushed off the incident in his book The Audacity of Hope, saying "It wasn't the Gulag".
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