The bodies were buried without family members' permission, it added.
Military spokesman Brig General Rabe Abubakar told the BBC the army had not killed anyone.
Reports of the deaths sparked outrage among Shia around the world and Iran called for their protection.
HRW said Nigeria's army version of events "does not stack up" and called for an independent judicial investigation into what happened.
The Shia have rejected a committee set up by the government to look into the incident, saying it would be biased.
"At best it was a brutal overreaction and at worst it was a planned attack on the minority Shia group," HRW Africa direction Daniel Bekele said.
The military accuses the pro-Iranian sect of trying to assassinate army chief Gen Tukur Buratai, which it denies.
It also released images purportedly showing Shia with sticks and some throwing stones at them when they tried to pass through a makeshift roadblock erected by the group.
But Human Rights Watch says there has been no "credible information" that any soldiers were injured or killed.
It is difficult to determine an accurate death toll but the information was gathered from hospital sources and eyewitnesses, the campaign group added in a statement.
Nigeria's Islamic spiritual leader, the Sultan of Sokoto, has warned that the raids on the sect, known as the Islamic Movement of Nigeria (IMN), could spark a new insurgency.
Militant Sunni Islamist group Boko Haram has killed thousands of people in its pursuit of an Islamic state, and has attacked the IMN.
The IMN said the military had destroyed its religious shrine and the home of its leader Sheikh Ibraheem Zakzaky during the raid.
Sheikh Zakzaky is currently being held by the police.
Those killed during the incident include the group's deputy leader and its spokesman.
Last year, three sons of Sheikh Zakzaky were killed in clashes between the army and pilgrims in a religious procession.
Shia in Nigeria
Published: 2015-12-24 14:00:00