The London-listed songs investment fund owns the rights to back catalogues of stars including Michael Bublé and Shakira, and takes in the royalties the artists would have received from streaming services.
Founder Merck Mercuriadis, a former manager to Beyoncé, labelled the Digital, Culture, Media and Sport Committee's report on the economics of streaming, released on Thursday, "impressive".
The report warned that "pitiful returns" are impacting the "entire creative ecosystem" - and said even top artists are seeing "meagre" royalty payments each time songs are played on platforms such as Spotify and Amazon.
MPs called on the Government to introduce a system where performers have a right to receive a share without reference to their label contracts.
The inquiry also raised "deep concerns" about the position of the major music companies in the market, and called on the Government to refer the case to the Competition and Markets Authority (CMA) to launch a market study into the "economic impact of the majors' dominance".
Mercuriadis backed the calls to refer the issue to the CMA, and said: "This is essential to ensure that the unhealthy control that the major recorded music companies have over streaming negotiations is addressed and to expose the fundamental flaws that exist within the music industry."
A Government spokeswoman welcomed the report and said ministers will issue a response "in due course".
Hipgnosis has raised more than £1 billion since floating in 2018, has been on a recent buying spree, and last week revealed it has raised another £156 million to buy more catalogues.