The 2-0 victory for the French champions was made a lot easier by some woeful defending by United.
Phil Jones allowed PSG to counter for the first goal by jumping in for a tackle inside the opposition's half and then could not block Matuidi's close-range finish.
And Ibrahimovic was allowed to walk through a static back line and convert Maxwell's cross in the 34th minute.
After recording three decent victories, United headed back to England after a chastening defeat that reminded them much work has to be done if they are to get back on a par with Europe's elite.
Senior sources at United insisted earlier this week that Van Gaal was happy with his defensive options, but on this evidence, the Dutchman may need to rethink.
United, who were without PSG target Angel Di Maria, started relatively well. Bastian Schweinsteiger looked eager to answer his critics, of whom one was Van Gaal.
The German swept up the field and lofted a ball to Wayne Rooney, who squared to Memphis Depay but he shot wide.
Schweinsteiger showed no mercy to Ibrahimovic, knocking the Swede off the ball. The forward rolled around on the turf, but received no sympathy from the crowd or the referee.
Ibrahimovic rose to his feet and put PSG ahead. He was helped in no small part by Jones.
The centre-back tried - and failed - to dispossess Ibrahimovic 10 yards inside the PSG half. Jones had only just managed to track back to the edge of the area by the time Lucas Moura had lofted a brilliant pass to Matuidi and he slotted in before the England defender and Luke Shaw could intercept.
United's defending was just as inept for the second goal. Maxwell found space on the left to square for Ibrahimovic, who strode past two defenders and slotted past a hesitant De Gea.
Some of PSG's passing was a joy to watch. Lucas Moura, Maxwell and Ibrahimovic all exuded flair.
United, on the other hand, were deteriorating as the half went on. Ashley Young and Rooney misplaced passes. The only time United tested Kevin Trapp was from a Depay free-kick.
Van Gaal replaced Schweinsteiger, Young and De Gea with Morgan Schneiderlin, Andreas Pereira and Sam Johnstone at the break.
Pereira, who has impressed for United on this tour, made an immediate impression, crafting a lovely ball into the box for Juan Mata, but the Spaniard miscontrolled.
The Brazilian then found Rooney, who knocked the ball down to Depay but his shot did not trouble the PSG goalkeeper.
Michael Carrick's poor pass allowed Youssouf Sabaly in at the death, but he shot wide and PSG settled for a 2-0 win.
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