The Genovese club said team captain Domenico Criscito, Davide Biraschi and Darian Males had joined the 14 teammates who had tested positive since Sept. 27.
The tests then had led to the postponement of Saturday’s Serie A game against Torino.
Five Genoa staff members are also said to be positive.
Atalanta did not give the name of the individual affected, nor did it specify if it was a footballer or a staff member.
A note on its website spoke of an asymptomatic case with “a low COVID-19 viral load.”
The ANSA news agency reported that the Saturday press conference of coach Gian Piero Gasperini had been called off.
Atalanta are to host Cagliari on Sunday.
Napoli, who met Genoa last weekend, said on Twitter that Macedonian midfielder Elif Elmas was positive after swab tests taken Saturday.
The Neapolitans announced on Friday that their Polish midfielder Piotr Zielinski was positive.
Napoli visit champions Juventus on Sunday.
Napoli players had been left out of the latest Italian national squad pending negative test results.(dpa/NAN)