The clashes came after rights groups accused police of beating the 28-year-old activist Khaled Mohammed Said to death in the northern port city of Alexandria early June, Reuters reported on Monday.
The violence began when some 200 demonstrators tried to break through a police cordon on Sunday.
According to a security official, police forces detained 32 protesters in the rally.
Activists said the victim was killed after attempting to expose police corruption. They asserted that undercover officers beat him to death after he posted an internet video showing police officers sharing the profits of a drug deal.
Police denied the charge and said the young man died of an overdose of narcotics.
Egypt's authorities ordered an autopsy and referred the case to Alexandria's court of appeal for further investigation.