Payments companies have become attractive targets for buyout groups and credit card firms seeking to take advantage of a switch from cash transactions to smartphone or mobile payments.
Permira will acquire the Klarna stake from existing shareholders General Atlantic and DST Global, and the Sweden-based firm's co-founder Niklas Adalberth.
General Atlantic and DST Global will cease to be shareholders in Klarna after the deal, they added in a statement.
Klarna, which says it handles 650,000 transactions per day, got a banking licence from Sweden's financial watchdog last month, two weeks after Anders Holch Povlsen, owner of Danish fashion retailer Bestseller, bought a stake.
Permira's investment in Klarna follows a move by a consortium of Blackstone (>> Blackstone Group LP) and CVC Capital Partners <CVC.UL> to buy payments processing company Paysafe Group (>> Paysafe Group Plc).
Many more deals have been announced over the past month, including French payments specialist Ingenico (>> Ingenico Group) buying Stockholm-based rival Bambora from Nordic Capital for 1.5 billion euros (1.31 billion pounds).
U.S. credit card processor Vantiv (>> Vantiv Inc) made a 7.7 billion pounds bid for Britain's Worldpay (>> Worldpay Group) and Danish payment services firm Nets A/S (>> Nets) said it had been approached by potential buyers.
(Reporting by Parikshit Mishra in Bengaluru and Clara Denina in London; Editing by Amrutha Gayathri and Alexander Smith)