Njorn, a Copenhagen-based company that has already started a similar initiative over the border in Denmark, says it plans to trace people in Sweden using illegal streaming websites by linking IP addresses (unique data linked to computer and tablet devices) with home addresses.
The crackdown is set to get underway in the summer and will focus on those logging on to sites including Dream Film, Swefilmer and Popcorn Time.
Njorn says its goal is to stimulate debate about sites which are not legal and could be detrimental to the global film industry. It says it represents a number of major players in the entertainment business.
"It is possible to say many nice things about the job losses due to piracy. But when communicating with young people who get everything to be free on the net, a letter with an invoice is a more efficient way to get a discussion going," lawyer Jeppe Brogård Clausen told Swedish technology site IDG.se.
The tactic is already common in Denmark where illegal streamers usually face fines of around 2,000 SEK ($231).
In Sweden, fines for this kind of internet crime are not common, but a man who watched more than 60 movies via the BitTorrent site was ordered to pay a large sum by the Swedish Supreme Court in December 2014 and Clausen said this could act as a precedent for future charges.
"We must plan so that it is done properly so that it does not become "negative goodwill" for the film companies," he explained.
"But the goal is that it should be like in the subway, if you do not pay then you run a risk if you take it," he added.
Piracy has long been a hot topic in Sweden, where the illegal Pirate Bay site launched 2003, allowing users to download music for free.
The Scandinavian nation adopted tough legislation and took legal action against the site while Swedish start-up Spotify launched the first major free music streaming site in the world, starting with a free ad-supported service followed by a subscription model.
The consumption of pirated movies and television shows shot up a few years ago, but dipped again as pay-per-view or pay-per-month services like Netflix and HBO Nordic arrived in the region.
However it is estimated that at least one million Swedes continue to download pirated movies.