Also, a group of Taliban suicide bombers attacked a government compound in southern Helmand province, killing three Afghans two policemen and a civilian.
The attacks came as the Taliban have intensified their spring offensive in a bid to undermine the Western-backed government as foreign combat troops prepare to withdraw from the country by the end of the year.
The attack on the Turkish workers came early in the morning in eastern Nangharhar province's district of Behsud, said Ahmad Zia Abdulzai, a spokesman for the provincial governor.
No one immediately claimed responsibility for the attack. The Afghan Interior Ministry said the explosives were strapped to a motorcycle, which was remotely detonated as the minibus drove by.
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In Ankara, the Turkish Foreign Ministry confirmed the casualties and said the Turks were employees of the EMTA construction company.
Turkish contracting companies have undertaken hundreds of construction projects in Afghanistan and at least four Turkish road engineers have been killed in attacks since 2004, not including Monday's deaths.
Turkey, which shares religious, historic and cultural ties with Afghanistan, is involved in NATO operations there but has refused to take on any combat missions in the country, fearing a Muslim backlash. Its troops are instead involved in providing security, in reconstruction and training in Afghanistan.