The fight reportedly broke out after one migrant accused another of trying to steal from him in the vast tent camp in San Ferdinando, which sits on the outskirts of the southern city of Rosarno.
The tent camp houses thousands of people who work largely in the area's orange groves.
As two policemen intervened, one of the migrants pulled out a knife and stabbed one of the officers, who shot him, the reports said.
There was no information given about the nationalities of the migrants involved.
Rosarno is notorious in Italy for the climate of tension between its seasonal workers — many of whom hail from sub-Saharan Africa – security forces and local residents, and has been the scene of repeated clashes.
Two days of unrest in 2010 prompted more than 1,000 Africans to flee the Calabrian town after clashes left 67 people injured, between migrants, police officers and locals.
Doctors Without Borders at the time fiercely condemned local attitudes towards the migrants, saying conditions in the Italian tent camps were often worse than in refugee camps in Africa.