 Paul Davey of Drowned in Sound wrote that the song "sits comfortably alongside" previous singles "Hang with Me" and "Dancing on My Own". Davey referred "Indestructible" to as "an example of a pop-innovator at the top of her game". Jonathan Keefe of Slant Magazine praised the song's production and named it one of Robyn's best singles. Keefe also named it the standout among the new songs on Body Talk. Christian Hoard of Rolling Stone gave it three and a half out of five stars, and wrote that "[Robyn] sings an uncommonly elegant Europop melody". Evan Sawdey of PopMatters compared the song negatively to the acoustic version, believing it was a bad choice to "swap out strings for synths". He wrote, "Robyn's voice gets lost amidst the laser lights, and its impact just isn't as strong". Sawdey, however, considered it "great [for] the dance floor".
