The anti-corruption investigators had originally sought a life ban against the two most powerful men in football over a two-million-franc ($2-million) payment that Blatter authorized for Platini.
“The investigatory chamber intends to appeal against the decision for Mr Blatter and Mr Platini at the Fifa appeal committee,” said Fifa ethics committee spokesman Andreas Bantel.
The case is the latest in an escalating series of scandals since Swiss investigators detained several Fifa officials in Zurich on May 29th.
Blatter and Platini were suspended from all football activity for eight years by a Fifa tribunal on December 21st.
The ethics judges rejected corruption charges but said the pair had abused their positions in making the controversial payment.
The ethics committee is split in two.
The investigatory chamber looks into corruption cases while its adjudicatory chamber acts as judges.
Blatter and Platini have denied any wrongdoing and vowed to make appeals to Fifa as well as the Court of Arbitration for Sport and even Swiss courts if necessary.
Platini lodged his appeal at Fifa on Monday, his entourage said.
Blatter, who has led Fifa for 17 years, said the payment to Platini, the president of Europe's governing body Uefa, was for consultancy work carried out between 1999 and 2002.
They have said there was only an oral contract for the accord but insisted it was legal.
“There was no evidence of any corrupt conduct and the Fifa Adjudicatory Chamber got it right in that regard,” said Blatter's US lawyer Richard Cullen.
“Some members of the Investigatory Chamber were disappointed that their theory was rejected for lack of evidence and we remain confident that the facts demonstrate Mr. Blatter and Mr. Platini's conduct was appropriate in all respects and that the appeal committee will agree,” he added.
Blatter, 79, was to stand down at a Fifa congress on February 26th when a special election is to be held.
He wants to clear his name so he can officiate at the assembly.
The suspension devastated 60-year-old Platini's hopes of becoming Fifa leader.
The Frenchman announced last week that he was withdrawing from the Fifa race to concentrate on clearing his name.
Fifa's appeal committee rarely reduces sanctions imposed by the governing body's ethics or disciplinary panels.
In 2013 the appeals committee increased an eight year term ordered against Vernon Manilal Fernando, a former Fifa executive committee member from Sri Lanka, to a life ban.
The withdrawal of Platini has left five candidates for the Fifa presidency: Asian Football Confederation president Sheikh Salman Bin Ebrahim Al Khalifa, Uefa general secretary Gianni Infantino, South African tycoon Tokyo Sexwale, former Fifa vice president Prince Ali bin al Hussein from Jordan and a former Fifa official Jérôme Champagne.
The corruption scandals have grown with 39 individuals and two companies now facing charges in the United States over more than $200 million in bribes paid for sports contracts.