It is understood that the trio had all reported feeling unwell which led to the entire Sri Lanka squad being tested, with the positive results coming back on Wednesday.
It brings the number of Covid-19 cases in the Sri Lanka camp to five, following Angelo Mathews – who was the first and had to be subbed out on the third day of the first Test – and then left-arm spinner Praveen Jayawickrama, who will also miss the second Test.
Mathews, however, has completed his isolation period and is available for selection. Oshada Fernando, who was Mathews’ Covid sub, will now be in line to replace Dhananjaya, whose absence means Sri Lanka also lose a spin-bowling option.
Offspinner Lakshitha Manasinghe and left-armer Prabath Jayasuriya had also previously been added to the squad, while it was confirmed on Thursday that left-arm wristspinner Lakshan Sandakan has also been called up.
Australia are staying in the same hotel as the Sri Lanka team, but are keeping their distance, and at this point, have had no positive tests on the tour.
Australian players are tested daily outside of matches, while rapid tests are only taken when players feel ill during a Test match.
AAP contributed to this report