In a Thursday interview with Italy's Corriere della Sera, Hollberg complained about being unceremoniously "fired" as a result of a "counter-reform" by the government.
"On the eve of Friday August 9th, I learned in an email from the [Culture] Ministry that I would be out of a job from August 22. Fired," the German historian said.
Hollberg had expected to stay until the end of her contract in November.
"It's all so absurd, in June I was offered an extension. I was not given any reason for the current decision," she said separately to dpa.
Hollberg was one of several foreign experts hired in 2015 to run top public cultural institutions, following a reform by a previous centre-left government.
The reform allowed selected Italian museums to be run by externally-recruited experts, rather than Culture Ministry officials, and gave them more autonomy in a bid to modernize governance.
The changes have been credited for making museums less bureaucratic and more attractive to the public. Hollberg said yearly visits to her museum rose by 22 per cent, to 1.7 million, in the last three years.
But the government that took office last year - and collapsed this week - opposed the reform, and outgoing Culture Minister Alberto Bonisoli, of the Five Star Movement (M5S), worked to partly undo it.
Specifically, Hollberg was pushed out because the Gallerie dell'Accademia lost its independence and was merged with the Uffizi, another famous Florence museum run by a German, Eike Schmidt.
She called the merger a mistake because "the Uffizi are a Medici-era museum and we are not, we are something else and we need to have different management."
Schmidt, whom Hollberg reproached for not expressing solidarity, is also leaving his job this year, but his decision was taken in 2017, well before the Bonisoli "counter-reform."
However, other foreign Italian museum directors have announced plans to leave the country, citing hostile government attitudes as the reason.
One is Peter Assmann of Austria, who is due to leave as director of the Palazzo Ducale in Mantua in November to head the Tyrolean State Museum in Innsbruck.
"The tone against us foreigners has become increasingly harsh. We are not wanted anymore," Assmann told German magazine Der Spiegel last week.
He said he did not like the nationalist rhethoric used by the ruling parties, especially the far-right League of outgoing Interior Minister Matteo Salvini, who often uses the slogan "Italians first."
"I see parallels with the seizure of power by the fascists before World War II. Salvini postures and talks like Mussolini. It's all clearly staged," he added.
The M5S-League government collapsed this week, and it is not clear whether it will be replaced by another administration or if there will be snap elections later this year.
In her comments to dpa, Hollberg said political interference in cultural affairs was "a great danger," and brought up the example of the communist German Democratic Republic (GDR).
She accused the M5S-League government of leaving behind "a trail of destruction" with its decision to end the autonomy of the Gallerie dell'Accademia and of other institutions.
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