The Eintracht Frankfurt midfielder was among the original shortlist of 10 but the downsized three announced by the world football governing body on Monday did not have the attacker's name.
The three, from which the eventual winner will be selected, were decided by votes.
The winner of the award, which seeks to honour the scorer of the best goal of the 2016-17 campaign, will be announced at the London Palladium on October 23.
Playing for Spanish club Las Palmas against Villarreal last season, Boateng finished off a neat play build-up with a sublime effort at Estadio de la Ceramica.
Tana Dominguez back-flipped a ball into the box and the German-born made no mistake with his attempt, acrobatically hitting a shot on the volley to give the Yellows a first half lead.
The goal, however, could not fetch UD the desired points as the home side equalised and registered the winner after recess.
The former AC Milan enforcer is the third Ghanaian to have been nominated for the Puskas Award after Michael Essien and Emmanuel Agyemang-Badu in 2009 and 2012 respectively.