Rugani said he was "fine" despite testing positive for the virus with Juve confirming on Friday (AEDT) that 121 people connected to the club — including players and directors — are undergoing voluntary isolation.
The club's UEFA Champions League Round of 16 tie with Lyon has been postponed as European football continues to respond to the pandemic, which has killed more than 1,000 people in Italy.
Juve donated €300,000 ($537,330), jointly given by the club and players, to begin the fundraising efforts, with money set to go to the 'Piedmont Region-Coronavirus emergency support' initiative.
Club chairman Agnelli asked fans in a video released via social media to donate to the fundraiser, which is hosted on the GoFundMe website.
"In this moment of a medical state of emergency, we too, as Juventus, want to make our contribution," Agnelli said.
"First of all, by respecting the rules and asking everyone to do the same: stay home.
"Since yesterday, I too am observing a period of voluntary isolation, but we have to and want to do more.
"And that's why, along with our players, we have launched a fundraising campaign to support our healthcare professionals in our neighbourhoods - in Turin and Piedmont.
"And that's why we ask you to contribute. In this difficult time, despite being distant, let's stay united and all together. We will get out of this delicate moment."
Juve is not set to play again until next month with all sporting activity in Italy suspended until 4 April (AED).