The cases, from among the playing squad and other staff, were confirmed following the 6-0 league defeat to Napoli on Monday (AEST).
"The club has activated all the procedures as per the protocol and informed the authorities. The club will give updates as the situation evolves," a club statement read.
This news means Sunday's (AEST) scheduled game against Torino could now be in doubt.
It also means Napoli will likely need to carry out tests of its squad before Monday's (AEST) clash with champion Juventus.
Sampdoria also confirmed on Monday that forward Keita Balde had tested positive for COVID-19 and will now follow the necessary health protocols.
The player is due to join Sampdoria from Monaco this week on loan.