The ministry introduced a bill proposing that "people who want to change their legal gender are no longer required to undergo medical treatment."
The bill is expected to pass with a broad majority in parliament.
"Norway is in the forefront when it comes to LGBT [lesbian, gay, bisexual and transgender] rights. But our current system for changing legal gender is unacceptable and has been unchanged for nearly 60 years. This proposal is in accordance with human rights," Healthcare Minister Bent Høie said in a statement.
The bill "is historic because it is now the individual and not the health services that decide when he or she has changed legal gender," he said.
As in many other countries, people who want to officially change sex in Norway must currently undergo a long slew of procedures that usually take many years.
They have to go through in-depth psychiatric tests, hormone treatments and surgery for irreversible sterilisation.
"It's a very intrusive process," said Patricia Kaatee of Amnesty Norway.
The bill to be submitted to lawmakers states "that a person who feels that their gender differs from the sex they were given at birth, has the right to change this based on their own experience," the health ministry said.
People will have to fill out a document and send it to the nearest tax office, which registers civil status.
"It's the same procedure that has existed for changing your name since 2008. You can even do it in one click on the Internet," Ingvild Endestad of Norway's LGBT association said.
The age requirement to change gender will be lowered from 18 to 16, with no parental authorisation required.
For minors aged six to 16, parents will be required to authorise the change. If one parent opposes, authorities may decide "in the child's best interest."
Children under the age of six will only be allowed to change gender if the child was born with a doctor-certified "genital ambiguity".
Amnesty International hailed the bill as a "historic breakthrough for transgender rights", and urged the Norwegian parliament to vote in favour of it to end "decades of discriminatory practices."
Norway would become one of the most liberal countries in the matter.
Argentina has since 2012 authorised gender changes by declaration only.