But in May this year, despite what the Constitution says, the Turkish Parliament approved the lifting of immunity of 138 MPs, including those of the HDP.
Today's arrests are particularly significant as MPs had been until now spared from a wave of detentions in Turkey's restive Kurdistan.
Last week, the two co-mayors of the main Kurdish city of Amed (Diyarbakir), Gultan Kisanak and Firat Anli, had also been arrested.
Besides, several media in both Kurdish and Turkish languages have been closed down.
Sirri Sureyya Önder, one of the HDP MPs that had taken a more active part in the —now cancelled— peace talks between the Turkish government and PKK imprisoned leader Abdullah Öcalan, has also been arrested.
the arrest of the 12th MP, Imam Tasçier.
According to Hürriyet newspaper citing sources of the Amed Prosecution Office, arrests have taken place within the framework of an investigation in which MPs are being accused of "terrorism" and of carrying out "propaganda" on behalf of the Kurdistan Workers' Party (PKK), the Kurdish political and military organization that since the 1980s has maintained an armed conflict with the Turkish state.
The HDP denies those accusations.
Some MPs belonging to main Turkish opposition party CHP (Kemalist, secular), also said the arrests amount to a "coup."
CHP leader Kemal Kiliçdaroglu said Turkey is heading towards a "dangerous direction."
Since the July failed coup, the CHP had closed ranks with Erdogan's AKP regarding the need to ensure the security of the current Turkish system and to address the dangers that, according to the two main Turkish parties Turks, are threatening the country.
As of last month, however, the CHP again began to speak up against Erdogan, whom it blames of seeking to implement a "caliphate." The Kemalist party opposes Erdogan's attempt to implement a presidential system in which the AKP leader would accumulate further power.