"Given the news priority over matters unrelated to 'Julieta', we at (production firm) El Deseo have decided to call off the photo call and junket planned for tomorrow," it said in a statement.
The scandal erupted on Sunday when media groups made public a year-long worldwide investigation into a trove of 11.5 million documents leaked from a Panama-based law firm that allegedly expose a tangle of offshore financial dealings by the elite.
Among those involved are friends of Russian President Vladimir Putin, the brother-in-law of Chinese leader Xi Jinping, football star Lionel Messi, Iceland's Prime Minister Sigmundur David Gunnlaugsson - who resigned Tuesday - as well as Almodóvar and his brother Agustin, the co-founders of El Deseo
In a tweet, Agustin Almodóvar said the junket had been cancelled due to the "pressure" they were under but he said that scheduled one-on-one interviews would go ahead.
Atención a la gente preocupada por la promoción de #Julieta.Hemos cancelado un photocall por la presión que tenemos y mantenemos entrevistas— Agustín Almodóvar (@AgustinAlmo) April 5, 2016
According to the online daily El Confidencial, which revealed part of the leaked documents, the brothers gained control of an offshore company based in the British Virgin Islands in 1991, though it is unclear whether the firm ever had any funds.
In a statement, Agustin Almodóvar acknowledged that the firm was created "ahead of the possible international expansion of our company."
But "the firm was left to die without having been active as it did not fit with our way of working."
"I deeply regret the damage made to my brother's public image, caused exclusively by my lack of experience in the first years of our family firm," he adds.
"In any case, I reiterate that both my brother Pedro and I, as well as our production firm, are up to date with all our tax obligations."
The press junket had been set to take place Wednesday in Madrid, just two days before "Julieta" comes out in Spain.
The drama, which stars Spanish actresses Emma Suarez and Adriana Ugarte, tells the life story of a woman whose daughter inexplicably left home when she turned 18 and has given no sign of life for over a decade.