Immigration Minister Chris Evans said the decision had been made "in the light of changing circumstances" in those countries.
He added that the move would "send a strong message to people smugglers".
Correspondents say a recent increase in the number of asylum seekers arriving by boat has put pressure on the Australian government.
Rights group Amnesty International called the decision "an appalling political move".
Friday's announcement came as news emerged that the navy had intercepted a sinking boat with 70 people on board off Christmas Island in the Indian Ocean, where Australia has a detention centre.
'Hardline approach'
More than 100 boats carrying asylum seekers have been intercepted by the Australian navy since the current government came to power in 2007.
Many of them are carrying people from Sri Lanka and Afghanistan.
Mr Rudd has been under mounting political pressure over the rise in the number of boat people, says the BBC's Nick Bryant in Sydney.
The immediate suspension on the processing of visa applications from new Afghan and Sri Lankan asylum seekers is clearly intended as a deterrent.
But our correspondent says the decision is being widely interpreted as a political move to neutralise an always sensitive issue ahead of this year's election.
"We have taken a consistently hard-line approach to people smuggling and today's announcements will further strengthen the integrity of Australia's immigration system," said Mr Evans.
Boats will not be turned away by the Australian navy and boat people will still be taken to a detention centre at Christmas Island.
However new arrivals will not be able to apply for asylum.
The Australian government says it will review the situation for Sri Lankans after three months, and for Afghans after six.
Amnesty International urged the Australian government to explain why it believed security conditions in the affected countries had improved enough to justify suspending asylum claims.
"Sadly it appears that the government has caved in to political pressure and is now attempting to override the rights of the most vulnerable to score political points," said Andrew Beswick, of Amnesty International Australia.
BBC News
