Amnesty said in a report that tens of thousands of students - known as "talibes" - "are forced to beg" as part of a system to bring teachers income.
They also suffer health problems such as malnutrition, skin diseases and often have "huge abscesses in their mouths" from unsanitary conditions and lack of care.
The students also "face abuses from some Koranic teachers and their assistants," the rights group said in the report.
Teachers told Amnesty that "shackling is a common practice, particularly for runaways, in order to prevent their escape. "
In the Muslim-majority nation where religious leaders wield wide social and political influence, poor children have long been entrusted to Koranic schools, called daaras, for their education.
While there are no official statistics, estimates suggest there are more than 2,000 daaras with almost 200,000 talibes.
"Some 25 percent of these are thought to be forced to beg," Amnesty said, quoting a so-called mapping exercise in 2018 by the NGO Global Solidarity Initiative (GSI).
Amnesty said forced begging amounted to trafficking involving teachers and students not just from inside Senegal but also from neighboring countries such as Gambia and Guinea-Bissau.
It said Senegal has passed its own laws and signed international conventions to protect children but "these regulations fail to be properly enforced due to social pressure."
A new draft law on the status of the daara that aims to incorporate the Koranic schools into the national education system faces tough opposition from some Koranic teachers who view it as "an anti-Islamic attack," Amnesty said.
"An important draft Children's Code also remains blocked due to pressure from conservative quarters," it added.
"Faced with the suffering of many talibe children, we are calling on the authorities to take strong action by adopting the draft Children's Code and the law on the status of the 'daara'," it said.
Authorities have in recent years launched several operations to rescue children from the streets, including students attending the schools.
Senegalese President Macky Sall held a meeting with influential Koranic teachers last month where some urged the release of "dozens" of colleagues jailed over claims they had abused students.
One case three years ago saw several detained for chaining up truants.
Sall has promised funding for Koranic schools as well as greater recognition for teachers with Arabic language qualifications.