The probe was opened after receiving complaints from four women, who claim that they have been sexually harassed by Pūkas, the Prosecutor General's Office said.
The lawmaker denies these accusations and says that he will not step down as a member of the Seimas.
The prosecutors said that a group of parliamentarians and a public organization had formally asked them to investigate the sexual harassment claims.
According to the Criminal Code, "a person who, in seeking sexual contact or satisfaction, harasses a person subordinate to him in office or otherwise by vulgar or comparable actions or by making offers or hints shall be considered to have committed a misdemeanor and shall be punished by a fine or by restriction of liberty or by arrest".
The Info TV channel earlier this month cited a female Vilnius resident as saying that during a job interview, Pūkas invited her to visit his room in the Seimas hotel and to see his bedroom and made remarks about the "fun of rolling in his bed."
More women later told the media that they had experienced inappropriate conduct by the man.
The Seimas on Thursday opened impeachment proceedings against Pūkas on suspicions that he might have breached the oath and violated the Constitution.
Pūkas was elected to the Seimas on the Order and Justice list, but he left the party's political group in the parliament after sexual harassment allegations were made public.