The track marks the second release from her Greatest Hits...So Far!!! LP, which entered at number five on the UK album chart and number 14 in the US last month.
The 'Who Knew' singer revealed she was shooting the promo earlier this month, tweeting: "alright peoples!! mama's fired up this morning! workout, shoot a commercial, a video... all very exciting stuff. no sex crimes though (sic)."
Images of the star on set have since leaked online, and reveal her wearing a grey ball gown.
The track was officially released to US iTunes yesterday, where it landed at number 50. A clean version of the track, called 'F**kin' Perfect (Perfect)' has also been made available.
Pink's last single 'Raise Your Glass' became her third single to top the US Billboard chart.