Southeast Turkey is an area predominantly populated by Kurds, where Ankara is conducting an operation against the PKK, which it considers to be a terrorist organization.
His Swedish counterpart, Margot Wallstrom, says "the arrests could risk fueling the already existing tensions in the country".
The BBC's Mark Lowen in Turkey says that the arrests represent a major escalation of a clampdown that has seen Kurdish media closed down and the mayor of Diyarbakir arrested.
NTV television said the pair were accused of spreading propaganda for the outlawed Kurdistan Workers Party (PKK) while Anadolu said Demirtas was accused of provoking violence in deadly protests in October 2014.
Media reports said the explosion could be heard from several parts of the city and caused damage to nearby buildings.
Yildirim also said one of the assailants was "caught dead", but did not elaborate. The head of the HDP's faction in the Turkish parliament, Idris Baluken, was also held.
The interior ministry said Friday's detention orders were for 13 members of parliament, but two were overseas and were therefore not immediately detained.
The others are in court waiting for their rulings. "Otherwise you'll butcher democracy in Turkey".
The government introduced a nationwide state of emergency after a failed military coup on July 15 which gave it broad powers to round up suspects linked to the putsch. "There is nothing I can not answer for", Demirtas said in a statement to the prosecutor, which was shared by HDP lawmaker Besime Konca.
As part of the investigation, Demirtas was detained at his Diyarbakir residence on the same grounds.
Anadolu reported the lawmakers were detained for not appearing in court to testify in ongoing terrorism-related investigations. The HDP rejects the accusation.
In response to the arrests, Germany's Foreign Ministry was quoted as saying there can be "no justification for muzzling or even imprisoning the political opposition".
Parliamentarians in Turkey normally enjoy immunity from prosecution, but the immunity of many lawmakers, including HDP deputies, was lifted earlier this year. "Again. Now HDP members of parliament are being detained", the European Parliament's Turkey rapporteur, Kati Piri, said on Twitter of a country that is seeking membership of the EU.
Twitter, Facebook, YouTube and Whatsapp were reported to be inaccessible inside Turkey shortly after the detentions, even when users tried to circumvent restrictions using a virtual private network (VPN).
Rights activists say restricting access to the internet is aimed at preventing calls for demonstrations.
Those detained include the co-chairs of Turkey's pro-Kurdish party and other senior officials. "Called EU ambassadors meeting in Ankara", Mogerhini tweeted.
Hours after Mr Demirtas was arrested in Diyarbakir, a huge vehicle bomb killed eight people and injured more than 100.
A large explosion, believed to be caused by a vehicle bomb, hit the largest city in Turkey's mainly Kurdish southeast region on Friday.
Earlier, Prime Minister Binali Yildirim had mentioned eight deaths, including two police officers and six civilians.
A total of nine people were martyred in terrorist group PKK's vehicle bomb attack on a police station in the largest city in southeast Turkey on Friday. The state-run Anadolu Agency said one person was killed and some 30 others were wounded.
The attack took place at around 8 am local time (05:00 GMT) near a building used by riot police. The Diyarbakir governor's office said the outlawed Kurdistan Workers' Party, or PKK, had claimed the attack.
The Diyarbakir governor's office said that it was a vehicle bomb attack that took place at about 8am local time (5:00 GMT), blaming Kurdish fighters.