"The request for political asylum was lodged two days ago via a fax sent to the Italian embassy," Bonino said in an address to parliament.
"The rules require that the asylum-seeker needs to present himself personally" either to the embassy or on Italian territory, she said.
"The conditions are not there to accept it, nor is it possible for the Italian government from a political point of view," she said.
Snowden is believed to have been stuck in the transit zone of Moscow's Sheremetyevo airport since June 23, as he tries to avoid US justice for leaking details about a vast US electronic surveillance programme.