Gamers have taken to social media and forums like Reddit to express anger over the so-called "cross-play" problem. Players can sign up for a "Fortnite" account. Those who have done that on a PS4 have reported not being able to use that same account on the Switch.
That means any in-game purchases or progress they have made in "Fortnite" will not be carried over to the Switch. Nintendo's console allows players to play on a TV but then continue the progress on a tablet like device.
Sony shares were down over 2 percent after the backlash.
"I was a tester on PC whos (sic) finished every season and spent hundreds of dollars on the game but nope no Switch play for me since I played once on a PS4," on person on Reddit wrote.
Such limitations don't exist when playing on Microsoft's Xbox One first and then the Swtich.
A Sony spokesperson was not immediately available for comment when contacted by CNBC, but issued a statement to the BBC explaining how it has 80 million monthly active users on its PlayStation Network and is always interested in hearing feedback from the gaming community.
"We also offer Fortnite cross-play support with PC, Mac, iOS, and Android devices, expanding the opportunity for Fortnite fans on PS4 to play with even more gamers on other platforms," the spokesperson said.
"We have nothing further to add beyond this at this point."
A spokesperson for Epic Games, the developer behind "Fortnite" was not immediately available for comment when contacted by CNBC.
The game was initially released last year on a number of platforms including the Xbox One and PS4. Earlier this week, "Fortnite" was released on the Nintendo Switch, and in under 24 hours, it was downloaded more than 2 million times, according to Nintendo of America president Reggie Fils-Aime. Epic Games confirmed in a blog post on Tuesday that there are now 125 million players of "Fortnite".
It has become somewhat of a viral hit with a strong fan following.
The cross-play issue could be damaging for Sony as it looks to further cement its leading position in the games console market. The Japanese electronics giant has sold 76.6 million PS4s versus the Xbox One which has sold 39.1 million, according to IHS Markit data. Some users on Twitter said they would stop using their PS4.
This week, both Microsoft and Sony had strong showings at E3, the world's largest gaming conference. But the "Fortnite" issue could overshadow some of the blockbuster games that Sony showed off and hoped would build excitement for the year ahead.
A Microsoft executive took the opportunity to take a swipe at Sony.