"This has been a fighting issue for the human rights organisations, women's organisations and many members of parliament for years," she said.
Parliament is expected to vote on the plan before Iceland's general elections on April 25, the minister said.
Prostitution was legalised in Iceland in 2007 in order to protect prostitutes and make it easier for them to seek assistance and go to the police without fearing recrimination.
The ban on buying sex is aimed at hitting users of prostitutes.
According to the bill currently being discussed by parliament, anyone who purchases or promises to purchase sexual services can expect fines or up to one year in jail.
If the person they are purchasing sexual services from is under the age of 18, they risk up to two years in prison or fines.
Iceland's Nordic neighbours Norway and Sweden have already introduced such bans on buying sex.
Gudrun Jonsdottir, a spokeswomen for Stigamot, the Icelandic counselling and information center for survivors of sexual violence, hailed the action plan.
"We have now shown that we understand the connection between pornography, prostitution and human trafficking," she told AFP.
Strip clubs are as a general rule forbidden in Iceland but are allowed to operate with special permission from local authorities. The new legislation would abolish that exception.
Iceland has been hit by a deep recession after the spectacular collapse of its banking sector six months ago.
The economic crisis made the new legislation even more necessary, Johannesdottir stressed.
"In times of economic downturn, it is even more important to tackle this issue. When there are economic hardships there is an even greater danger of criminal activity, like human trafficking and sexual abuse," she said.
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Image from http://go.hrw.com.