The opposition party said Löfven did not assume responsibility as Sweden's leader during the IT security breach and failed to realize the seriousness of the scandal.
Sweden Democrat representative Paula Bieler called for the vote in parliament. She said Löfven, as prime minister, was ultimately accountable for what happened but has dodged questions concerning his responsibility.
"He has talked about disasters but not about the disaster in his own government offices, that information wasn't passed along, and his role as the leader in that," Bieler said in parliament.
Her view was echoed by Sweden Democrat Aron Emilsson, who told Radio Sweden that the responsibility for the scandal lies at the prime minister's door.
"It's a scandal that has shaken the whole Swedish political discussion where the prime minister has great responsibility."
The scandal concerns the government Transport Agency which outsourced IT services in a way that allowed individuals abroad, who lacked security clearance, to handle classified information like the national vehicle and driver's license register. The government was criticized for not acting quick enough or passing the news along through proper channels.
Two ministers eventually resigned in the wake of the scandal.
The no-confidence vote is likely to come on Friday but right now it lacks support from other opposition parties. Center Party leader Annie Lööf has said her party would not back a no-confidence vote and the other three main oppositions parties have remained cool to the idea.
Defence Minister Peter Hultqvist is also facing a vote of no-confidence this week thanks to the scandal though his fate is also unclear, since the Sweden Democrats said they would not support the vote unless other opposition parties joined them on the no-confidence vote against Löfven.