Education and Childcare Minister Elizabeth Truss said an over-reliance on calculators meant children were not being given a strong grounding in mental and written arithmetic, and students should only use calculators once they have a grasp of basic mathematical skills.
"All young children should be confident with methods of addition, subtraction, times tables and division before they pick up the calculator to work out more complex sums," Truss said.
Teaching unions responded, calling the ban "a retrograde step."
"It is entirely appropriate for children in primary school to learn to use a range of tools to solve math problems and the skill of deciding which tool and method to use for a particular problem is an important one," said Christine Blower, general secretary of the National Union of Teachers.
"It may not be appropriate to use calculators for the whole of the math test paper, but it is a retrograde step to ban them completely as it will diminish the skills set for primary pupils and leave them floundering in secondary school," she said.
The government's move follows its review of calculator use in primary schools, the BBC reported.