Musically, "Peek-a-Boo" was described as an up-tempo pop dance song with addictive hooks. Meanwhile, Tamar Herman of Billboard stated that it is "laden with trop house elements underneath the overarching quirky pop vibe, and is driven by a deep bass drumline, scratchy synths, and metallic beats" which also features "a variety of diverse, playful instrumental elements nestled beneath the main melody". The song is considered as their fourth single under their "Velvet" persona, and was composed in the key of C# minor, with a tempo of 115 beat-per-minute. To match the mysterious vibe of the music video, member Joy recorded her own laughter multiple times for a segment in the track but ultimately, the voice taken from the original demo was featured instead. Its lyrics, which were written by SM Entertainment songwriter Kenzie, compares a newfound romantic relationship to a mischievous game children play.
