The two Japanese citizens were in their eighties and had underlying health conditions, according to Japanese public broadcaster NHK.
News of the deaths come after it was confirmed British nationals who were stranded on the vessel will be flown home on an evacuation flight on Friday.
Around 500 passengers have left the ship, which is docked in Yokohama, after a two-week quarantine that failed to stop the spread of coronavirus among passengers.
NHK said the deceased passengers were an 87-year-old Japanese man and an 84-year-old Japanese woman.
Kyodo news agency reported 29 people were in a serious condition, including one who had earlier tested negative for the virus.
The health ministry could not immediately confirm the reports.
At least 621 people on the Diamond Princess tested positive for the virus. This is the biggest cluster of cases outside mainland China.
There were 78 British passengers on the cruise liner when cases of the coronavirus strain known as Covid-19 started to emerge.
Four British cases have since been confirmed by the Foreign Office.
Couple David and Sally Abel, who have highlighted their plight on social media, are among those to test positive for the potentially deadly virus.
It was unclear whether they will be able to board the repatriation flight tomorrow.
Foreign Secretary Dominic Raab said last night that an aircraft departing on Friday will bring the stranded Brits who have registered for the flight home.
He urged other British nationals on board the ship in the port of Yokohama who are still seeking to leave to contact the Foreign Office.
Mr Raab added: "We will continue to support British nationals who wish to stay in Japan."
Those repatriated will be quarantined at accommodation at Arrowe Park on the Wirral on their return, a Department of Health and Social Care spokesman said.
Anyone who develops symptoms during the flight to the UK will be taken to hospital, while it is understood any pre-existing cases will be treated in Japan.
Passengers were yesterday allowed to begin leaving the ship but authorities said it could take several days for all 3,700 to disembark.
Meanwhile, the European Commission has announced the EU will be financing the repatriation of citizens from any of the EU27 still stuck on the vessel.