As close contacts of the person with the positive result, the whole touring group was required to self-isolate and take Covid tests.
All 39 people in the touring group associated with the Breakers, including children, underwent PCR tests yesterday, which uncovered a further three positive results.
That means the touring group will remain in lockdown isolation and undergo further PCR testing until further notice.
The four Covid positive members of the touring group have not required hospitalisation.
"Our team has followed best practices, but unfortunately, a number of individuals have experienced symptoms," said Breakers owner Matt Walsh, who is with the team in Australia.
"We will continue to follow the advice of medical professionals and the NBL and look forward to being back on the court soon."
Last Friday, Victoria eased Covid restrictions for the fully vaccinated ahead of the state reaching its 90 per cent vaccination milestone.
Altogether 827 people tested positive for the virus in Victoria today, while there are 9420 active cases in the state.