The inquiries are part of the "fight against terrorism, which continues with determination everywhere.
The inquiries are part of the "fight against terrorism, which continues with determination everywhere, including on social networks", the ministry said in a statement.
After a coup attempt in July, Turkey declared a state of emergency and launched deep purges of perceived opponents, sparking concern among human rights groups which accuse Ankara of repression.
More than 1,600 people accused of "propaganda or apologising for terrorism" or "insulting state officials" have been arrested in the past six months, according to the ministry.
Turkish authorities are often accused of restricting access to social networks after serious incidents, such as attacks, to stop the circulation of information that could "undermine state security".
Access was severely disrupted after the assassination on Monday of Andrei Karlov, Russia's ambassador to Turkey.
And Twitter and YouTube have slowed since the publication on Thursday of a video in which the Islamic State group purportedly burned alive two captured Turkish soldiers.
An internet monitoring body, Turkey Blocks, also reported difficulties accessing virtual private networks which are routinely used to circumvent restrictions on access to social networks or websites.