Gattuso was informed of the news as he took Napoli through training on Tuesday, with Serie A aiming for a June 20 restart following a three-month suspension as a result of the coronavirus pandemic.
Back in February, Gattuso had to abandon a post-match news conference after a 4-2 victory at Sampdoria, when he was told that his sister has been taken ill and hospitalised.
Francesca previously worked as a secretary at Gattuso’s former club AC Milan, who led the tributes to their ex-employee with a statement on twitter which read: "Francesca Gattuso faced her illness with the same strength and energy she brought to Milanello [Milan's base] and Milan every day.
"Rino [Gennaro], the immense pain you and your family are feeling is also ours. Rest in peace, dear Francesca."
"The Gattuso family will always be in AC Milan's heart," the team added.
"Rino had passed his passion for Milanello on to Francesca and she always embraced and cherished the Rossoneri values."
Gattuso’s current club Napoli, on behalf of president Aurelio De Laurentiis, waved in with a tribute of their own.
It read: "Aurelio De Laurentiis, with his wife Jacqueline and children Luigi, Edoardo and Valentina, the managers, the technical staff, the team, all of Napoli and Filmauro [Napoli's parent company], strongly embrace Rino Gattuso and join him in his immense pain for the loss of his sister, Francesca.
"We are all close to you with a dear heart, Rino."
