PSG had won the competition five years in a row and had not lost a domestic fixture this season but were undone when Guingamp grabbed the winner from the spot in stoppage time.
Marcus Thuram missed Guingamp's first penalty after 61 minutes, and Neymar headed home two minutes later to put the home side 1-0 up.
Yet Yeni Ngbakoto levelled with Guingamp's second spot kick after 81 minutes and then Thuram netted in the third minute of stoppage time to give Guingamp, who currently sit bottom of Ligue 1, a sensational win.
Neymar, Edinson Cavani and Marco Veratti were all booked in the dying seconds as the PSG players protested at not being awarded their own penalty when Veratti went down in the box.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Guingamp are joined in the last four by Girondins de Bordeaux, who beat Le Havre 1-0, and AS Monaco, who overcame Rennes 8-7 on penalties after the sides drew 1-1.
Strasbourg reached the semi-finals on Tuesday with a 2-1 win over Olympique Lyonnais.
Guingamp's win was the shock result of the season so far and ended PSG's 20-game unbeaten run in all domestic French competitions.
The capital club lead Ligue 1 by 13 points and are also in the last 32 of the French Cup.
It was a massive tonic for the Brittany side, who extended their encouraging run to four consecutive wins.
Although they are bottom of Ligue 1 they won their last two cup fixtures before Wednesday and also beat second bottom club AS Monaco in the league.
(Reporting by Andrew Downie; Editing by Toby Davis)
