"All of them were Christian students. They go in buses like that to Mosul's university after the troubled times when Christians were targeted in the past," Nissan Karoumi, the mayor of Hamdaniya, said.
Dr Muhsin Shamzi, who works at a hospital in Irbil, said at least 17 critically injured patients were taken to the hospital.
About 750,000 of Iraq's 30 million population are Christians.
The US-based National Council of Churches last week sent a letter to Hillary Clinton, the US secretary of state, calling on her to urge Iraqi officials to do more to protect Iraq's Christian community.
The organisation said they were particularly worried now as Iraq struggles to seat a
government after the March 7 parliamentary elections.
"Our concern is now particularly acute because it is possible that tensions will increase as various political forces continue to vie for power following the recent elections,'' the letter said.
"We fear that a growing climate of mistrust and animosity will further threaten the fragile Christian community."
In November, the US-based Human Rights Watch warned that minorities including Christians were the collateral victims of a conflict between Arabs and Kurds over control of disputed oil-rich provinces in northern Iraq.
While sectarian violence has dropped dramatically across Iraq since its peak between 2005 and 2007, attacks remain common, especially in Baghdad and Mosul.