Ukraine prosecution officials said there was no evidence of a crime but one politician called for the president to face impeachment proceedings.
Eleven million documents from Mossack Fonseca show how some of its clients use it to avoid tax and launder money.
The firm says it did nothing illegal.
The Panamanian firm is alleged to have set up a company in the British Virgin Islands for Mr Poroshenko called Prime Assets Partners, which describes itself as a holding company of the Roshen confectionery group. Before becoming president, Mr Poroshenko had been known as the "chocolate king".
During his presidential campaign in 2014, Mr Poroshenko vowed to sell most of his business assets. He won the election and was sworn in in June 2014. The assets were transferred to the newly created holding company.
In October 2014 a Ukrainian bank, of which Mr Poroshenko owns a controlling stake, sent a letter of recommendation to Mossack Fonseca saying that his accounts had been "conducted properly up to our satisfaction", according to the International Consortium of Investigative Journalists.
Journalists from the Organized Crime and Corruption Reporting Project (OCCRP) argued that President Poroshenko's action might be illegal on two counts: starting a new company while president and not reporting the company on his disclosure statements. The BBC cannot independently confirm this.
Anti-corruption group Transparency International also believed that the "creation of businesses while serving as president is a direct violation of the constitution".
But a spokesman for Mr Poroshenko said the company it set up for the president had no active assets and was part of a legitimate corporate restructure aimed at helping to sell the Roshen group. None of the three associated accounts held more than â‚¬2,000 (Â£1,600; $2,270), he said.
The Ukrainian leader went on Facebook to insist that, on becoming president, he had delegated management of his assets to consulting and law firms.
"I believe I might be the first top office official in Ukraine who treats declaring of assets, paying taxes and conflict of interest issues profoundly and seriously, in full compliance with the Ukrainian and international private law," he wrote.
Legal firm Avellum, which was given the task of selling Roshen, said that using a company with foreign jurisdiction was the only way to move the company into a blind trust. "Any allegations of tax evasion are groundless," it told Reuters news agency.
However, Oleh Lyashko, head of the populist Radical party which had earlier been part of the governing coalition, called for impeachment proceedings to be initiated, although that was unlikely to take place.
Ukrainian President Petro Poroshenko says he did nothing wrong, after leaked documents suggested he had set up an offshore company as a tax haven using Panamanian legal firm Mossack Fonseca.