PRO14 has postponed all Round 14 and 15 fixtures involving Benetton and Zebre due to restrictions on travelling implemented by the Italian government.
The decision affects the Round 14 game between Cardiff Blues and Zebre and the Round 15 game between Munster and Benetton, due to be held in Wales and Ireland respectively.
There are now six Italian fixtures that need to be rescheduled due to fears over the coronavirus.
"PRO14 Rugby has been consistent in ensuring that it has the latest information and guidance made available by the local and national authorities via our participating unions in the UK, Ireland, Italy and South Africa," the organisation said in a statement.
"As previously indicated, PRO14 Rugby aims to reschedule these matches on dates during the European weekends in April and May. PRO14 Rugby is currently engaged with EPCR to avoid any scheduling conflicts with European knock-out games."
If no alternative dates can be found to hold the games, the board of Celtic Rugby DAC has agreed that both teams will be awarded two points and the game will be marked as a 0-0 draw.