Ahmad Obali, a prominent proponent of Azerbaijani nationalism in Iran and virulent critic of the Islamic Republic, refused to speak about who might have attacked him.
Local rights activists say hundreds of religious Shias have been arrested in recent weeks as pro-government media report on the arrests of "spies" and "traitors" working for neighboring Iran.
His outspoken criticism of Iran, and the timing coinciding with the opening of Azerbaijan's embassy in Israel led some fellow MPs to point the finger at Tehran.
The drills included a crossing of the river that forms the Azerbaijan-Iran border, mirroring the threat that Iran’s armed forces had made weeks earlier.
Questioning the territorial integrity of the neighboring country, once a taboo topic, is increasingly entering official discourse both in Baku and Tehran.