In a statement in Spanish obtained by the International Consortium of Investigative Journalists and translated by Sky News, the firm explained why it was closing.
It described itself as "the victim of a cyberattack on a global scale" and said it could no longer operate because of the attention brought on it by the leak.
Following the publication of the documents in 2016, many politicians resigned amid public protest. Stories of tax evasion led to raids and investigations in dozens of countries.
The firm has always stressed that it was the victim of a crime as documents leaked to media organisations across Europe allegedly revealed how the rich and famous exploited secretive offshore tax regimes.
It was the world's fourth biggest offshore law firm at the time of the leaks, and one of its founders, Ramon Fonseca, said that the data breach was a "crime" and an "attack" on Panama.
He said: "This is a crime, a felony. Privacy is a fundamental human right that is being eroded more and more in the modern world."
The firm's offices were raided in El Salvador, although in its statement the company said: To this day, nowhere where Mossack Fonseca holds companies have criminal proceedings been initiated for the provision of this service."
In its letter explaining the shut-down, the firm said: "The deterioration in reputation, the media campaign, the financial siege and the irregular actions of some Panamanian authorities has caused irreparable damage."
This damage "has resulted in the total cessation of operations to the public at the end of this month after 40 years of growth and contribution socially, economically and culturally to our country", it added.
The firm criticised the attention the firm had been paid in Panama, stating: "Only in Panama are there investigations which, unfortunately, have not been handled adequately despite us, from day one, providing all the information that was required by the authorities."
The firm said that as a result of the Panama Papers it had to "begin the process of reducing its offices and personnel and in total now has less than 50 employees".
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