They argue that increased control of social media will also limit Turkish access to independent or critical information in a country where the news media is in the hands of government-friendly businessmen or controlled by the state.
"Why now?" asked Yaman Akdeniz, professor at Istanbul's Bilgi University and also a cyber rights expert.
"While print and broadcast media platforms are already under government control, social media networks are relatively free. Social media has become one of the few spaces for free and effective expression in Turkey," he told AFP.
Human Rights Watch expressed concerns that the law would enable the government to control social media, to get content removed at will and to arbitrarily target individual users.
"Social media is a lifeline for many people who use it to access news, so this law signals a new dark era of online censorship," said Tom Porteous, deputy program director at Human Rights Watch in a statement before the legislation passed.
The legislation has aroused deep concerns for many Internet users in Turkey who mobilised online in recent weeks using the hashtag "don't touch my social media".
'No obstacle'
Ibrahim Kalin, President Recep Tayyip Erdogan's spokesman, brushed off fears the law would hamper free speech.
"There is no obstacle to social media users freely expressing their opinion," he told CNN-Turk television on Tuesday.
"Here is the rule: whatever is a crime in the real world is also a crime in the cyber world ... there must be a limit to criticism."