"I think Nyo Thein May, 11, was hit accidently by security forces when they fired warning shots to disperse people," Pol Lt Col Min Aung said by phone from Sittwe, 500 kilometres north-west of Yangon.
The girl was staying at the World Food Programme's office in Sittwe, when it was set upon by Buddhists Wednesday night who pelted the homes of several relief organisation with stones.
Police fired above the heads of the crowd to disperse them late Wednesday night. Nyo Thein May was allegedly hit by a stray bullet.
She died in hospital Thursday, Min Aung said.
A 6pm to 6am curfew was imposed in Sittwe on Thursday, said Sittwe officials, who described the city as "quiet."
The incident was sparked Wednesday night after an American relief worker took down a Buddhist religious flag from her rented residence.
The flags are a symbol of protest against an upcoming census, which Rakhine Buddhist residents have opposed.
Both the United States and European Union condemned the attacks on the foreign aid workers in Sittwe.
"We are very concerned by the wave of hostilities targeting international organisations which provide essential assistance to local communities and the most vulnerable in the Rakhine State of Myanmar," said Kristalina Georgieva, EU Commissioner for International Cooperation, Humanitarian Aid and Crisis Response.
Earlier this month, Medicins Sans Frontiers (MSF) was ordered to suspend its operations in Rakhine state following local protests against its alleged support of Rohingya villagers who had been attacked by Rakhine Buddhists.