Trail Blazers president Neil Olshey said the decision to temporarily shut down the facility was made "out of an abundance of caution." The team didn't reveal whether the positive tests involved players, coaches or executives.
"Over the past four days, we have had three positive COVID test results within our organization," Olshey said in a statement Sunday. "Out of an abundance of caution, having completed contact tracing, we are closing our practice facility today for deep cleaning while we run confirmatory tests."
Sunday was supposed to have been the first full day of training camp for the Trail Blazers. Portland, along with all other NBA teams, started welcoming players back to its facility for individual workouts last week.
The Blazers didn't say how long their training facility would be closed. It is the first facility shutdown in the league since players returned last week.
Portland is scheduled to begin its preseason slate at home Friday against the Sacramento Kings.
NBA teams started coronavirus testing to prepare for training camp at the end of November. The league said 48 players -- about 9% of all tested -- were positive for COVID-19 in the first wave of that program.