They are in Armagh, Ballymena, Lisburn, Magherafelt and Strabane. David Ford had previously announced the closure of Limavady Courthouse.
He told the assembly on Monday that his decision was based on "unprecedented financial pressures" and the underuse of courthouses.
He also cited falling staffing levels.
"In common with other public sector organisations, the Department of Justice has seen very significant budget reductions in recent years," said Mr Ford.
"These reductions have had, and will continue to have, a significant adverse impact upon the entire justice system, including the Courts and Tribunals Service."
The Law Society said the closures will undermine the justice system.
Its president, John Guerin, said the move will leave those who need it most without access to their local court.
"Court closures will cause greater disruption, inconvenience and unnecessary stress to court users and those seeking access to justice," he said.
"The reality is that a reduced court infrastructure will mean an increased volume of cases being spread across a more limited range of court venues resulting in the potential for overcrowding and delays of business."
In November 2015, a report on Northern Ireland's courts recommended that a number of them should be closed.
The recommendations were in a paper published by the Northern Ireland Courts and Tribunals Service (NICTS), which was given to the justice committee.
North Antrim DUP MLA Paul Frew described the announcement as "yet another kick in the teeth" for Ballymena.
The justice minister has announced that five Northern Ireland courthouses are to close.