"We have reached the conclusion that there is not enough recent progress in our bilateral agenda with Russia to hold a US-Russia Summit," the White House said in a statement.
In addition to Russia's "disappointing decision" to grant Mr Snowden temporary asylum, the White House cited a lack of progress on issues ranging from missile defence to human rights.
"We believe it would be more constructive to postpone the summit until we have more results from our shared agenda," the White House said.
The decision to cancel the US-Russia summit comes the day after Mr Obama appeared on an evening chat show, The Tonight Show with Jay Leno, in which he condemned a newly enacted anti-gay law in Russia.
"I have no patience for countries that try to treat gays or lesbians or transgender persons in ways that intimidate them or are harmful to them," Mr Obama said.
But the White House reaffirmed Mr Obama's commitment to attending a forthcoming round of G20 economic talks, which take place on 5-6 September in the Russian city of St Petersburg.
In the wake of the announcement, Mr Putin's foreign affairs adviser Yuri Ushakov said it was clear the US had cancelled the meeting over the Snowden affair.
In a conference call on Wednesday, Mr Ushakov added the Kremlin was disappointed by the move and that the invitation for talks remained open.
"Russian representatives are ready to continue working together with American partners on all key issues on the bilateral and multilateral agenda," Mr Ushakov said.