The paper, citing a source close to the case, said the IT employee had been placed in provisional detention on suspicion of removing a large haul of confidential documents.
The spokesman for the Geneva's prosecutor's office, Henri Della Casa, told AFP that a criminal case had been opened following a complaint filed by Mossack Fonseca.
He declined to comment on whether an arrest had been made.
According to the paper, the unnamed employee is suspected of inappropriately accessing a database, stealing assets and abusing his position.
Della Casa neither confirmed nor denied those details.
Le Temps said it had no information on whether the arrested individual was the so-called "John Doe" who has claimed credit for the unprecedented leak in April of 11.5 million Mossack Fonseca documents.
The documents revealed the names of leaders, politicians, celebrities and wealthy individuals from around the world who used the Panama-based firm to create offshore entities to hide their assets.
The explosive dossier linked some of the world's most powerful leaders, including Russian President Vladimir Putin, British Prime Minister David Cameron and others to unreported offshore companies.
Offshore companies are not in themselves illegal, but the sudden publication of troves of data drew attention to rampant tax avoidance and even money laundering crimes.
Consequences from the leak continue to reverberate worldwide, with investigations under way in several countries.
The European parliament last week launched a far-reaching probe into potential tax fraud in Europe that was sparked by the Panama Papers scandal.
Last month, Mossack Fonseca said it was filing a lawsuit against the International Consortium of Investigative Journalists (ICIJ) which coordinated a global probe by multiple media outlets into the information contained in the Panama Papers.
The firm's Geneva office did not respond to queries from AFP seeking details of the criminal case in Switzerland.