The 39-year-old Buffon was a key member of the Juventus side that reached last season’s Champions League final, but he missed out on a first winner’s medal as the Italians were beaten 4-1 by Ronaldo’s Real Madrid in Cardiff.
The shortlist was decided by the 80 coaches of the clubs that played in the Champions League and Europa League group stages, as well as 55 journalists.
Five-time Ballon d’Or winner Lionel Messi has won the award twice, as has Portuguese forward Ronaldo.
Since its inception in 2011, unlike other similar individual awards, the UEFA accolade has not been totally dominated by Ronaldo and Messi.
Spain midfielder Andres Iniesta won the honour in 2012, followed by French winger Franck Ribery a year later.
Real Madrid, who have lifted the European Cup in three of the past four seasons, had four players in the top 10, with Luka Modric fourth, Toni Kroos fifth and Sergio Ramos seventh.
Argentinian forward Paulo Dybala (sixth) joined his Juve team-mate Buffon in being named, while Monaco’s rising teenage star Kylian Mbappe, Bayern Munich striker Robert Lewandowski and former Manchester United forward Zlatan Ibrahimovic rounded out the top 10.
Luis Suarez, who scored 37 goals for Barcelona in all competitions last season, missed out, as did his former team-mate Neymar, who has since joined Paris Saint-Germain in a world-record 222-million-euro ($260.9m) move.