The parliamentary probe adds to pressure on the country's far-right interior minister amid reports that Western secret services are increasingly wary of sharing information with their EU ally.
Austria's far-right Freedom Party (FPÖ), which has governed in a coalition since late last year, has a "cooperation pact" with President Vladimir Putin's United Russia party.
Interior Minister Herbert Kickl is from the FPÖ, which also nominated Foreign Minister Karin Kneissl.
The inquiry is due to open with testimony from two officials of the BVT intelligence agency who complained about the February raids on offices and homes of senior officials.
Also due to appear was an official from the police unit that carried out the raids.
Officially, the operation related to an investigation into allegations of abuse of office.
But unusually, the searches were carried out by a police street crime unit run by an FPÖ official.
Files seized reportedly related to investigations into far-right extremist groups.
Last week, a Vienna court declared some of the raids illegal because prosecutors had failed to explore other avenues to obtain the evidence they were looking for.
Kickl, who as chief strategist masterminded the FPÖ's rise to power, has insisted the raids were above board, and accused the opposition of seeking to score cheap political points by calling for investigations.
Kickl is not due to give his statement to the inquiry until November.
Austria's National Security Council, an oversight body composed of ministers and opposition party representatives, held a closed-door meeting Monday to discuss the BVT affair.
Chancellor Sebastian Kurz of the centre-right People's Party at the helm of the governing coalition, insists that Austria, which holds the EU rotating presidency, sees eye to eye with the bloc when it comes to Russia.
FPÖ-backed Kneissl, however, raised eyebrows by inviting Putin to her wedding last month. Images of the two of them dancing circulated widely.