The song contains an upbeat opening sequence with a heavy guitar riff. Tom Breihan from Pitchfork Media wrote that the song "begins with über-processed new wave guitars that sort of sound like the Cars". According to a digital music sheet published at Musicnotes.com by Sony/ATV Music Publishing, "Shut Up and Drive" is written in the key of C♯ major and is set in simple time with a moderately fast groove.
The song starts off with an energetic introduction accompanied by a distinctive guitar riff. According to Tom Breihan from Pitchfork Media, the opening section bears a resemblance to the Cars' style. The sheet music published at Musicnotes.com by Sony/ATV Music Publishing reveals that "Shut Up and Drive" is composed in C♯ major and has a simple yet fast-paced rhythm.