Gobbetti has been credited with boosting Burberry's market value by a third as he has taken the brand further upmarket. Concern that his departure will undo some of that progress sent its London-listed shares tumbling as much as 10% in early trade while Ferragamo rose 2.3% in Milan.
Burberry recovered some of those losses to trade down 7.7% at 20.80 pounds. Ferragamo reversed early gains and was down 1.5% down at 19 euros, with one trader citing reduced likelihood of a takeover after Gobbetti's appointment.
"The board and I are naturally disappointed by Marco's decision, but we understand and fully respect his desire to return to Italy after nearly 20 years abroad," Burberry Chairman Gerry Murphy said in a statement.
Ferragamo, which became famous for shoes worn by Hollywood stars such as Audrey Hepburn, said Gobbetti would take up his new position once released from his contractual obligations.
Burberry said it will now begin the search for the 62-year-old executive's successor.
Known for its trench coats and trademark plaid, Burberry's strategy shift under Gobbetti injected fresh life into its ranges, helped by his 2018 recruitment of star designer Riccardo Tisci, a fellow Italian and former colleague at Givenchy.
"With Burberry re-energised and firmly set on a path to strong growth, I feel that now is the right time for me to step down," Gobbetti said.
The market, however, appeared less confident in Burberry without Gobbetti.
"This is a negative for Burberry and a source of uncertainty until we get clarity on the new CEO," Citi analysts said.
Citi predicted that Gobbetti's key initiatives will remain in place for at least another year and be executed by an interim CEO, possibly finance chief Julie Brown.
They also flagged potential uncertainty over creative director Riccardo Tisci, who had followed Gobbetti to Burberry.
Analysts were also puzzling over Gobbetti's decision to leave Burberry, which is more than three times bigger than Ferragamo by market value, though Hargreaves analyst Susannah Streeter suggested the reason could simply be that he wanted to return home after all the turmoil of the COVID-19 pandemic.
"Even chief executives, with access to first-class travel or private jets are not immune to quarantine rules and travel restrictions," she said.
Speculation over a management shake-up at Ferragamo has been circulating for some time, even after the Ferragamo family that controls the company confirmed current boss Micaela Le Divelec in her role as recently as March.
In Gobbetti, it has hired an industry veteran who has also led luxury groups Celine, Givenchy and Moschino. He took charge of Burberry in mid-2017 from fashion designer Christopher Bailey, who spent only three years leading the company.
Burberry said in May that sales were recovering from the coronavirus crisis, partly thanks to a rebound in China, but cautioned that profit margins would be dented by higher investment.
Hargreaves analyst Sophie Lund-Yates had noted that Burberry was set to come out of the pandemic in better shape than it had entered the crisis, helped by its repositioning at the more exclusive end of the luxury chain.
Ferragamo, meanwhile, has been hit harder than most of its rivals during the pandemic and is often cited by industry observers as a possible takeover target, though the Ferragamo family has denied that it wants to sell.
Graphic: Burberry shares -
($1 = 0.7190 pounds)
(Reporting by Muvija M and Claudia Cristoferi; Additional reporting by Agnieszka Flak; Editing by Louise Heavens and David Goodman)
By Muvija M and Claudia Cristoferi