James Murdoch, the former chief executive of 21st Century Fox, has taken a small stake in Vice Media, the irreverent media brand focused on millennials and entertainment.

Mr. Murdoch, who already sits on Vice’s board, made the investment as part of Vice’s recent acquisition of Refinery29, a women’s lifestyle publisher, according to a person familiar with the matter, who asked not to be named because the deal is meant to be private.

The investment, which was first reported by The Financial Times, is through Mr. Murdoch’s holding company, Lupa Systems. He formed Lupa after leaving 21st Century Fox, the media giant founded by his father, Rupert Murdoch. Last year, the family sold off the majority of Fox’s assets to the Walt Disney Company for more than $70 billion.

The younger Murdoch, who personally netted about $2 billion from that sale, has invested in a diverse group of media businesses that looks very different from the one his father founded. He is also less interested in traditional news ventures, the person who is familiar with the matter said.