Taliban spokesman Zabihullah Mujahid tweeted that Jalal had been detained Saturday over statements he made on social media in which he was "trying to instigate people against the system and was playing with the dignity of the people".
"He has been arrested so that others don't make similar senseless comments in the name of being a professor or scholar that harm the dignity of others," he added.
Mujahid shared screenshots of tweets he claimed had been posted by Jalal, which said the Taliban intelligence chief was a stooge of Pakistan, and that the new government considers Afghans as "donkeys".
In one television appearance, Jalal called Taliban spokesman Mohammad Naeem -- who was also participating -- a "calf", a grave insult in Afghanistan. Clips of his passionate criticism went viral on social media, sparking concern he risked Taliban retribution.
Jalal's wife Massouda, who once stood as Afghanistan's first woman candidate for the presidency, posted on Facebook that her husband had been arrested by Taliban forces and detained in an unknown location.
"Dr. Jalal has fought and spoken out for justice and the national interest in all his activities pertaining to human rights," she said.
A long-time professor of law and political science at Kabul University, Jalal has long had a reputation as a critic of Afghanistan's leaders.
On Twitter, rights group Amnesty International condemned the arrest of the lecturer "for exercising his freedom of expression and criticising the Taliban", calling for his immediate and unconditional release.
The Taliban have formed an all-male cabinet made up entirely of members of the group, and almost exclusively of ethnic Pashtuns. They have further restricted women's rights to work and study, triggering widespread international condemnation.