The Arab Organisation for Human Rights in Syria made this claim in a statement released in Damascus on Wednesday, a copy of which was obtained by Aljazeera.
In another statement, the rights group said a Canadian citizen returning home to Syria after years in exile had been arrested.
The students, from the northern province of Latakia, did not belong to any political party and it was not clear why they were detained, the statement said, adding that six of the students had been released.
Syrian authorities accused them of belonging to an organisation by the name of Sunaa al-Hayat, the statement said.
There was no official comment on the detentions.
In the second statement, the rights group said Syrian security forces arrested Maher Ahmed Zeidan, a Syrian who has a Canadian nationality, upon his arrival at Damascus airport on 21 April.
It called his arrest a violation of Syrian legal and constitutional norms, noting that the man decided to return home to take advantage of an informal amnesty for exiled citizens.
"Zeidan was not referred to a specialist court. Lawyers were not allowed to contact him," the statement said.
Though Syria has not formally declared an amnesty, Syrian diplomatic missions abroad were instructed last month to give passports to Syrians wishing to return home, and human-rights activists have said dozens of exiled Syrians have taken up the offer.