A student leader, identified as Rahul Pathak, died in firing in Morena district, Sub-Divisional Magistrate (SDM) Umesh Shukla told PTI.
Pathak was allegedly shot during protests by agitators and he succumbed to injuries enroute to hospital, he said.
As the violence escalated, curfew was imposed in the entire city, Shukla said.
Police said the protesters also stopped a train in Morena.
Curfew was imposed in Gwalior and Bhind districts also following violence, officials said.
Gwalior Commissioner B M Sharma said, "Curfew has been imposed in several parts of Gwalior city following violence during the protest."
However, Sharma did not share more details.
Eyewitnesses claimed that a person also suffered bullet injuries in the violence in Gwalior and was admitted in the hospital.
Curfew was also imposed in Bhind city, and Mehgaon, Lahar and Gohad areas of the district, Bhind Superintendent of Police Prashant Khare said.
Six people were injured in the firing by protesters in the district, he said.
The Army has been called in Bhind to control the situation, Khare said.
A report from Jhabua also said protesters looted shops during the agitation, triggering tension in the tribal town.
Meanwhile, Madhya Pradesh Chief Minister Shivraj Singh Chouhan appealed to the protesters to maintain peace in the state as the Centre has filed a review petition in the Supreme Court on the issue of dilution of the SC/ST laws.
Protests were also held in the state capital Bhopal with agitators blocking a road on the Board Office Square near the statue of Dalit icon Dr B R Ambedkar.
More than two dozen vehicles were damaged with several of them set on fire by the protesters during the protests in the state, eyewitnesses said.
In Morena district, the Chhattisgarh Express was stopped by protesters and was still stationed at the station, they said.