Tonev, on loan at Celtic from Aston Villa, was hit with the sanction by the Scottish Football Association, after being found guilty of racially abusing Aberdeen's Shay Logan.
The 24-year-old reportedly called Logan 'a black c***', something the BFU refutes along with Tonev, who is set to appeal the decision.
Pending an appeal, the two players could clash on Sunday, when Aberdeen hosts Celtic at Pittodrie Stadium.
"The Bulgarian Football Union would like to express its full support for the player," a statement read.
"We join Celtic and express our willingness to use every possible set of international football laws to reveal the truth.
"And, in this case, it is undeniable.
"A young and talented Bulgarian footballer is charged and punished for an offence he allegedly did not commit and [there is] no evidence of his guilt.
"Aleksandar Tonev [has] always been a role model, put his heart and soul on the field and never violated the principles of fair play in the football game.
"The Bulgarian Football Union strongly condemns all forms of racism and xenophobia in football stadiums and will continue its policy of zero tolerance for such events.
"In the case of Tonev, however, we demand to see evidence that he had committed that of which he is accused.
"Otherwise, we will consider that the penalty is biased and exaggerated."