The size of the stake and the amount paid have not been disclosed.
FlowNetwork delivers its programmes via the internet and supplies a number of Sweden's regional newspapers with technology and content. The company is co-producer of the new Swedish drama series Gåsmamman.
WPP, led by Sir Martin Sorrell, said the investment continued its strategy of developing integrated services in "fast-growing and important markets and sectors and strengthening its capabilities including digital media".
The company has set a target of 40 to 45 per cent of total revenue to be derived from digital in the next five years. Digital represented 36 per cent ($6.9bn or £4.6bn) of revenue in 2014.
The group saw a 5.1 per cent like-for-like jump in revenue in the fourth quarter.
WPP cited "strong growth in North America, the UK, and Asia-Pacific" in its earnings statement and singled out Burson-Marsteller, Cohn & Wolfe and specialist PR and public affairs businesses for strong performances. However, it said "H+K Strategies [was] more challenged".