The motion accused Napolitano, who is widely respected in Italy for fostering stability during recent economic and political turmoil, of "infringing the constitution" by overstepping his largely ceremonial role.
Roberto Speranza, chief lawmaker for the centre-left Democratic Party, said the move was "a crazy act aimed at undermining the basis of our democratic system".
The motion is virtually certain to be rejected as the Five Star Movement (M5S) does not have enough clout in parliament but it has inflamed political tensions.
The 88-year-old Napolitano helped set up Prime Minister Enrico Letta's current government and the previous cabinet led by economist Mario Monti, after billionaire tycoon Silvio Berlusconi's resignation in 2011.
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