Both the Swedish police and tax authority have claimed that the system has been widely misused and has aided the creation of a "shadow society".
Co-ordination numbers are a form of identity number issued by authorities for individuals who live and work in Sweden but who do not meet the requirements for being included in the country's population register.
Magadalena Andersson said the changes announced today will help "clean up" the system. "Today if you have a co-ordination number it's permanent so even if it's not used it's still in our registers. This we will change," Andersson told Radio Sweden.
However, the finance minister also insisted that there are widespread misunderstandings around the system and that it is not the coordination numbers in themselves that lead to crime.