The Browns were told about the positive test result Wednesday morning. All meetings will take place remotely as the team conducts contact tracing to identify any potential high-risk close contacts.
The Browns' campus is about 20 miles southwest of FirstEnergy Stadium in downtown Cleveland.
"The team will continue to consult with the league and medical experts on the appropriate next steps as the health and safety of our players, coaches, staff and the entire community remains our highest priority," the Browns said.
Wednesday's closure marks the third time in the last eight days that the Browns have closed their facility. The team has shuttered its headquarters six times since Nov. 13 to conduct contract tracing.
Five Browns players have tested positive for COVID-19 in the past three weeks. Browns defensive end Myles Garrett was activated Tuesday from the reserve/COVID-19 list. Fullback Andy Jankovich was activated on Monday from the reserve/COVID-19 list.
The NFL told teams last week that all in-person activities were prohibited Monday and Tuesday in response to a rise in COVID-19 positivity rates around the country and within the league.
The Browns will face the Tennessee Titans at 1 p.m. EST Sunday at Nissan Stadium in Nashville.