Fever Ray was lauded by music critics. At Metacritic, which assigns a normalised rating out of 100 to reviews from mainstream critics, the album received an average score of 81, based on 27 reviews, which indicates "universal acclaim". Graeme Thomson of The Observer described the album as "an astonishingly stark record" that is "[b]uilt on the barest of electronic bones and brought to life through Andersson's almost primal vocals, the songs search for a spiritual pulse amid soulless modernity." Ian Mathers of PopMatters stated the album is "not only as good as Silent Shout but [it's also] clearly akin to the sound she and her brother Olof perfected on that record", concluding, "Nothing that Fever Ray does is as immediate or soaring as a track like 'Marble House' but Fever Ray makes up for the lack of highs by being an even more all-enveloping experience than the last few Knife records." Similarly, John Doran of the NME commented that Fever Ray "has none of the immediacy of albums such as The Knife's Silent Shout, with its playful eclecticism and heavier, dancefloor-leaning beats. Most importantly, it doesn't have a killer hit single in the style of 'Heartbeats'", adding that in order to "fully appreciate this beautiful and understated gem, [...] it's important to relinquish all desires for another 'Heartbeats' and enter fully into the world of Fever Ray." Doran also called the album "magnetic and rewarding" and compared it to the likes of Kate Bush, Underworld and Yellow Magic Orchestra.
Pitchfork Media's argued that, in contrast to The Knife's "plasticky percussions and goofy synth sounds", Fever Ray "brims with fragile, more finely articulated sounds" and "moves at roughly the same pace and with the same general tone, rendering some of the songs indistinguishable at first, but committed listens will reveal this to be as nuanced and as rich of a production as anything either Dreijer has done."The A.V. Club 's Chris Martins viewed it as being "countless times more claustrophobic and creepy than Silent Shout" and stated that "[t]he vocal transformer is such a huge part of what Andersson does—androgynizing her words to accompany the cold music, mimicking the synth warbles and sustained tones that abound."The Independent critic Rupert Howe expressed, "Even beyond the gothic imagery and glacial electronics, this mesmeric solo project shares much with The Knife's last album Silent Shout", including "surreal lyrics" and "weird vocal treatments which pitch Andersson's voice down to a baleful masculine groan". Jonathan Keefe of Slant Magazine found that the album is "built upon contrasts. Most notably, Andersson's Fever Ray persona draws attention to her work as half of the Knife [...] Whereas the Knife is ostensibly a dance act, Fever Ray emphasizes tone over rhythm."
Alexander Tudor wrote for Drowned in Sound that "minimal beats on each track prove to have been constructed with incredible attention to detail, as are the smooth synth washes, and electronic simulacra of birdcall or animal noises. The tempo may be nightmarishly unvaried, track after track, but it's composed of glitches [and] bouncing balls", citing "Keep the Streets Empty for Me" as the album's best track. In a review for Allmusic, Heather Phares opined that "Fever Ray's mix of confessional lyrics and chilly, blatantly synthetic and often harsh sounds make this album as successful an electronic singer/songwriter album as Björk's Homogenic." Phares continued, "With almost tangible textures and a striking mood of isolation and singularity, Fever Ray is a truly strange but riveting album."Alexis Petridis of The Guardian felt that the album's "dolorous chords and stately rhythms recall the Cure, circa Faith, the glacial pace makes you think of the Blue Nile", noting that, "as unlikely a step as Fever Ray may seem for one of electronic music's most enigmatic figures, the results are triumphant."BBC Music's Chris Jones called the album "bloody marvellous", while observing "a vague sense of holding pattern here rather than massive innovation. Without brother Olof as a guiding hand on the droning sequencers the tunes fall a bit by the wayside", but wrote that "this very tiny drawback doesn't stop Fever Ray from being the kind of brilliant album that it may not make sense to play if you're prone to nightmares."
The Guardian named Fever Ray the second best album of 2009, calling it "[g]lacial, creepy and impish" and commenting, "Between the cavernous synths, the echoes and loops, the polyrhythms and snarling vocal processing, Andersson managed to capture the feeling of being totally alone while also projecting a childlike wonder." It was ranked the second best album of 2009 and twenty-fourth best album of the 2000s decade by Resident Advisor.The Sunday Times named Fever Ray the third best album of 2009 by a new artist and wrote that Andersson "responded to motherhood with an album of glacial sonic architecture, its unforgiving expanses conjuring up sleep-deprived mental churning", dubbing it an "electro classic".NME, Drowned in Sound and Pitchfork Media all placed the album at number nine on their respective lists of the Top 50 Albums of 2009, with the latter noting that "[w]hat's made Andersson's work even better is how her videos and performances amplify the music's sense of dread and mystery."
The album was listed at number sixteen on PopMatters' The Best 60 Albums of 2009, and the website opined, "Alternately chilly and warm, wistful and foreboding, expansive and claustrophobic, Fever Ray 's peculiarity and bleak magnificence holds us in its thrall." Online music service Rhapsody included Fever Ray at number twenty-two on its list of The 25 Best Albums of 2009. Slant Magazine named it the twenty-fourth best album of 2009, stating that Andersson "challenges the conventions of dance music with her distorted vocals and macabre imagery" the album "emerges as an unsettling, impossible-to-shake record that suggests the aftermath of when 'pop' truly bursts".iTunes US named Fever Ray the best electronic album of 2009 as part of the its Rewind 2009 roundup. It was included on Allmusic's Favorite Albums of 2009 and Favorite Electronic Albums of 2009 lists.
In 2010, Fever Ray won the P3 Guld award for Dance Artist of the Year, and was nominated for Newcomer of the Year and Pop Artist of the Year. The same year, she won a Manifestgalan for Best Live Artist and received a Beatport Music Award nomination for Best Electronica Artist.