Unai Emery's charges were thankful to braces from Giovani Lo Celso and Angel Di Maria, while Edinson Cavani and Julian Draxler also contributed to a humiliating evening for AS, who surrendered the league crown with five games still to play.
Victory for Les Parisiens sees the capital club earn their seventh Ligue 1 crown.
Monaco started with plenty of energy but almost fell behind inside nine minutes when Cavani collected at the back post, only to drag his volley across the face of goal and wide.
The hosts soon came back again through the striker, who spun a ball in behind for Dani Alves, allowing the Brazilian full-back to square across the face of goal where Lo Celso was free to slide home an opener.
PSG grabbed a second just a minute later too, Draxler threading Yuri Berchiche on the overlap, who was then able to cross for Cavani as the frontman rose above his marker to thump an unstoppable header beyond Danijel Subasic.
A period of outstanding attacking play was rounded off in the 20th minute when Cavani turned and hit a ball beyond the Monaco defence on the halfway line, which allowed Di Maria to scamper clear and lob Subasic with the deftest of chips to make it 3-0.
Monaco's first-half humiliation did not stop there, however, as youngster Lo Celso headed home his second of the night after profiting from an adroit one-two between Draxler and Javier Pastore on the left wing.
In a whirlwind first half, AS were able to grab themselves a slender lifeline when Berchiche was robbed by Almamy Toure, leaving the full-back to drill across goal and find Rony Lopes who lashed in at the back post.
Monaco should have grabbed another just after the break when Pastore played a suicidal pass across his own box, although Lopes could only fire straight at a grateful Alphonse Areola.
Having started slowly, PSG soon sprang back into life and they found a fifth in the 58th minute, Alves and Pastore combining beautifully on the break to play in Di Maria, who was clinical once more with his second clever finish of the night.
With the game all but wrapped up, PSG made it six with just under 15 minutes remaining when Falcao tracked backed to defend a corner, only to send the ball into his own net.
Things continued to get worse for Monaco too, Draxler capping off a standout showing by thumping home a late seventh to ensure that Paris made light work of Leonardo Jardim's men on their way to domestic glory.
PARIS SAINT-GERMAIN (4-3-3): Areola; Alves, Marquinhos, Silva, Berchiche; Lo Celso (Nkunku 80'), Rabiot (Diarra 65'), Draxler; Pastore, Cavani, Di Maria (Meunier 75')
MONACO (4-5-1): Subasic; Jemerson, Raggi, Jorge, Toure; Sidibe (Ghezzal 34'), Fabinho, Moutinho, Lemar, Lopes (Diakhaby 75'); Falcao (Tielemans 82')