Jay Z bought Tidal three years ago and his wife Beyonce and other artists own equity in the company.
Aiming to challenge larger rivals such as Spotify, Tidal offers artists on its platform more control over their music.
Sprint, which is owned by Japan's Softbank, will pay an estimated $200m (Â£162m) for a 33% stake in the company.
The deal means that Jay Z, whose real name is Shawn Carter, will make a return on the initial $56m investment he made when he bought Tidal from Norway's Aspiro in 2015.
Other artists including Madonna, Rihanna, Daft Punk, Kanye West and Jay Z's wife Beyonce are part owners of the service, giving Tidal a star-studded board of directors. It is reported that they will remain part of the company.
The investment could help bolster Tidal in its battle to win ground from Spotify and Apple, which dominate the fast-growing music streaming industry.
Sprint's decision to invest is a sign the mobile operator wants to provide its customers with more content in a highly competitive market. As a result of the deal, Sprint customers would have access to exclusive Tidal content.
Tidal has a 42 million song catalogue and is available in 52 countries, but is currently much less widely used than services from Spotify and Apple.
The American rapper Jay Z is selling a stake in his Tidal music streaming business to the telecoms company, Sprint.