Do Rabbits Wonder? received generally positive reviews from music critics. At Metacritic, which assigns a normalized rating out of 100 from mainstream critics, the album received an average score of 62, based on 13 reviews.
Heather Phares of AllMusic praised the band for displaying their idiosyncratic sludge rock with gusto and charm throughout the color-filled track list, concluding that the band's "major-label-level exposure is almost as refreshing as its noisy weirdness." Tom Moon of Rolling Stone praised the album for utilizing the punk blues formula set by The White Stripes and adding their own take on it, concluding that the result is "the kinetic rush of vintage punk minus the self-conscious nostalgia, the discipline of pop songcraft with, thankfully, no sugar added." Jason Jackowiak of Splendid was mixed about the album, saying that there were great ideas heard throughout but were brought down by the instruments taking away the songs' melody, concluding that, "Any hopes that their label boss/producer might plug in and inject some six-string vitality into the humdrum proceeding are dashed to bits as "Grey" fizzles out in a tempest of gargling mini-moog." Eric Carr of Pitchfork Media heavily panned the album, criticizing the band for being similar to Devo but with misused vocals and instruments that become incoherent arrangements that are hard to listen to, concluding that, "If nothing else can be said in its favor, this is music that will instantly, violently polarize people: some folks' inner masochists may welcome it as an alternative to self-flagellation; personally, I'd rather take sandpaper across my corneas than sit through this thing again." He also signaled out Jack White, V2 and Rolling Stone 's promotion of the band for the album's creation.