Police in the northwestern county of Telsiai said the federation filed the statement in the town of Mazeikiai on August 20.
Edgaras Stankevicius, the federation's secretary general, told BNS that the law-enforcement investigation concerned suspected match-fixing in Pirma Lyga, the second tier of the professional football championship.
"The police are carrying out their own pre-trial investigation, and our Investigative Committee is performing its actions. What I can confirm is that this is not about a single match and that this is a complex investigation," he said.
Stankevicius added that the match-fixing suspicions involve "not necessarily one football club".
"I can't comment on these things in more detail," he said.
The federation expects to provide more information in the next few weeks.