The singer released her seventh studio collection across the globe on November 19, but the album is yet to be available to legally stream anywhere online.
"Yes, what's going on?" one user asked on Spotify's forums. "I don't see the point of paying for Spotify if I'm not getting the music I desire."
Another added: "I can find the album, but none of the tracks are playable except for 'Diamonds'. The album is released, so why shouldn't we be able to play it with Spotify Premium?"
It follows Taylor Swift's recent decision to withhold her new album Red from online streaming services for the foreseeable future.
The country star's label Big Machine Records explained: "We're not putting the brand-new releases on Spotify.
"Why shouldn't we learn from the movie business? They have theatrical releases, cable releases. There are certain tiers. If we just throw out everything we have, we're done."
However, Sachin Doshi, Spotify's head of development and analysis, countered Big Machine Records's claim using Mumford & Sons' latest album Babel as an example of how streaming services don't affect physical and digital album sales.
The band's latest set was streamed over 8 million times during its first week on Spotify, but still managed to sell over 600,000 copies in the US and a further 159,000 in the UK during the same time.
"That goes to prove streaming services do not take away from unit sales and, in fact, can be additive for major artist releases," he told Rolling Stone. "That's our point and we're sticking to it."
Watch the music video for Rihanna's 'Diamonds' below:
Photo gallery - Rihanna performs at the Victoria's Secret fashion show 2012:
Copyright: Rex Features Startraks Photo/Rex Features