Cavani has scored 35 league goals in as many appearances in a stunning individual season, even though PSG are set to see their streak of four straight titles come to an end.
Their former striker Zlatan Ibrahimovic had won the award in three of the past four seasons, with Eden Hazard, Alexandre Lacazette, Karim Benzema and Didier Drogba also among the previous winners.
Leonardo Jardim was named Coach of the Year at the National Union of Professional Football Players (UNFP) ceremony on Monday, having led Monaco to the brink of the title.
Mbappe, meanwhile, scooped the Young Player of the award after a season that saw him develop into Europe's most wanted prospect, with 14 league goals and 11 assists playing a huge part in Monaco's stunning campaign.
The forward has been compared to Thierry Henry, who also scooped the young player award while at Monaco in 1997.
Danijel Subasic won the Goalkeeper of the Year award in another success for the Ligue 1 leaders.
And Chelsea star N'Golo Kante was recognised as the Best French player playing abroad, an accolade which Antoine Griezmann won in 2016.