The statement added that both players and the staff member were in good health and said the team had followed protocol and taken the appropriate measures following the results.
Suarez, who scored a penalty in Uruguay's 3-0 win over Colombia on Friday, is now ruled out of the match with Brazil.
He will almost certainly also miss his club's La Liga match against his former club Barcelona on Nov 21.
The Uruguayan is Atletico's joint-top scorer this season alongside Joao Felix, grabbing five goals since switching from Barca on a free transfer in September.
Suarez is the latest high-profile player to test positive for the virus during an international break, after Liverpool's Mohamed Salah was infected while on duty with Egypt.
Last month, Cristiano Ronaldo tested positive while representing Portugal and was forced to miss several games for Juventus.
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