Two former presidents of Spanish club Barcelona, Alexandre Rosell Feliu and Josep Maria Bartomeu Floresta, were also accused by the Prosecution Service in Santos, Neymar's home town.
The prosecution's statement said: "They forged a series of documents between 2006 and 2013 with the intention of reducing the taxes owed to the inland revenue in Brazil.
"Neymar's conduct, along with the others accused, caused millions in losses to the public coffers."
A judge must now decide whether the case goes forward.
The allegations refer to image rights contracts from 2006 when a teenaged Neymar was playing for Santos. Prosecutors allege further fraud occurred during negotiations to take him to Barcelona in 2011.
He eventually joined the Catalan side in 2013.
Prosecutors said the schemes involved three companies linked to the striker's family - Neymar Sport e Marketing, N&N Consultoria Esportiva e Empresarial and N&N Administração de Bens, Participações e Investimentos.
Neymar defended himself in a post on his personal website on Monday and said the prosecution was "seeking the limelight". He invited Prosecutor Thiago Lacerda to visit the offices of NR Sports to see the company for himself.
The prosecution has accused Neymar's father of designing schemes with the Spaniards as they negotiated his son's transfer.
"Between 2006 and 2013, the player's father was the principal mentor and mastermind of a series of contractual frauds involving Neymar's image rights, mainly through Neymar Sport e Marketing," the statement said.
Neymar signed several contracts with Santos and Barcelona to do publicity work but the money was paid into his father's accounts in order to reduce their tax burden, prosecutors allege.
They also said he provided false information on some contracts.
Earlier on Tuesday, both Neymar and his father – following on from Rosell and Bartomeu – appeared in front of a Spanish judge to give evidence about the alleged irregularities surrounding his transfer to Spain.
Rosell resigned as Barcelona chairman to defend himself against accusations that he and the club swindled Spanish tax authorities out of 13 million Euros.
A Sao Paulo judge also ruled last week that Neymar and his father must pay nearly 460,000 reais ($113,000) to Brazil's inland revenue in taxes owed from 2007 and 2008.
(Reporting by Tatiana Ramil; Writing by Andrew Downie; Editing by Peter Rutherford)
