The warning from ENAC, the national civil aviation authority, came after airlines resumed flights to many holiday destinations in countries balancing the need to attract tourists with fears of a resurgence in coronavirus cases.
Ryanair said in a statement that ENAC's assertions were "factually incorrect."
Italian rules require passengers to maintain distance from others unless other precautions are taken including controlled boarding and disembarkation to avoid close contact, temperature tests and the wearing of face masks.
But ENAC said Ryanair had systematically violated rules aimed at limiting the risk of contagion for passengers.
"Not only has the requirement for distancing between passengers not been observed but the conditions which allow an exemption have not been met," ENAC said in a statement dated Aug. 5.
If the "improper and disrespectful" failure to observe the regulations continued, it would stop exemptions to social distancing rules for Ryanair with the result that the company would have to operate flights at no more than 50% capacity.
Continued failure would result in Ryanair flights to Italian destinations being suspended, it said.
A Ryanair spokesman said the airline "complies fully with the measures set out by the Italian government."
"Our customers can rest assured that we are doing everything to reduce interaction on both our aircraft and at airports to protect the health of our passengers when flying Ryanair," the spokesman said in an emailed statement.
(Reporting by James Mackenzie; Editing by Keith Weir)