Leinster say that "an additional number of senior players" have tested positive for Covid-19 ahead of Friday's scheduled Champions Cup game against Montpellier in France.
Leinster postponed training on Monday as they waited on further test results.
Tuesday's Leinster statement did not elaborate on the amount of additional players who now must also self-isolate.
However, Leinster coach Leo Cullen later said that the Irish province are "fully intent of getting ready and playing the game".
"The HSE [Health Service Executive] has been informed in accordance with public health guidelines, as has EPCR [European Professional Club Rugby]," said the Leinster statement.
"The remaining members of the Leinster Rugby squad will train today in UCD and will continue to test daily and take all necessary precautions ahead of Friday's Heineken Champions Cup game against Montpellier in France."
Montpellier report fifth Covid positive
Montpellier, meanwhile, also reported a fifth positive Covid-19 in their squad on Tuesday.
A Montpellier statement said the latest Covid positive "considerably impacts the preparation for the match against Leinster Rugby scheduled for Friday, 17 December".
"In view of the latest results, the people concerned have been isolated and the team is now carrying out training in separate groups before being tested again this Wednesday."
Despite the Covid cases in their squad last week, Leinster began their European campaign by beating Bath 45-20 on Saturday.
Two Montpellier staff members tested positive last Friday before the French side's comprehensive 42-6 defeat to Exeter, while a further two players were also found to have the virus following the side's return from England.
Tuesday's Montpellier statement did not detail whether their latest Covid positive was a player or staff member.
Any cancellation of a Champions Cup match will result in a 28-0 win for the team deemed not responsible for a Covid outbreak.