According to Turkish website Zete.com, by 3 a.m. local time, over 2.4 million tweets had been sent from Turkey since the start of the ban.
The ban comes amid a corruption scandal in Turkey, which has seen Twitter full of tweets alleging government wrongdoing.
But Kroes added: "It's never acceptable - not before or after elections. We are talking about the values of our democracy."
Turkish telecoms watchdog BTK said Twitter had been blocked by the courts after complaints were made by citizens that it was breaching privacy, Reuters reported.
Turkish users are still able to tweet via text message, or SMS, however. Twitter highlighted the work-around on its @policy account late Thursday.
The ban in Turkey came on the eve of the eighth birthday of Twitter - one of the world's most popular social media websites, with more than 240 million active users.
The site has also proved itself as a key tool in recent struggles for democracy after playing a key role in the Egypt protests of 2011 - during which time the former government also tried to ban it, albeit unsuccessfully.
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