"Frozen" received critical acclaim from music critics, some of whom deemed it an album standout. It was described as being a masterpiece, and its melodic beat and sound were defined as "cinematic". The song was a worldwide chart success, peaking at number two on the US Billboard Hot 100, becoming Madonna's sixth number-two single and the artist with most number-two hits in the history of that chart, while it reached number one on the Hot Dance Club Play chart. It ultimately peaked at number one in the United Kingdom, Italy, Spain and Finland, and also within the top-five in other countries, such as Australia, Italy, Sweden and Switzerland.
The accompanying music video for "Frozen" was directed by Chris Cunningham in a desert in California, portraying Madonna as an ethereal, witchy, melancholy persona, shapeshifting into a flock of birds and a black dog. The music video received a MTV Video Music Award for "Best Special Effects" in 1998.