The Bhoys went down in within three minutes of the start as Alessandro Matri scored the opening goal of the night. Celtic gradually recovered to pose a threat at the other end.
However, despite creating many chances, Celtic suffered another blow in the 76thminute when midfielder Clausio Marchisio scored the second before striker Mirko Vucinic sealed the game netting the third in the 83rd minute.
PSG were on course to a famous victory when first-half goals from Argentine duo Ezequiel Lavezzi and Javier Pastore put the French side pole position, but their hopes were dashed in the dying minutes of the game.
Valencia full-back Adil Rami reduced their lead to half before Ibrahimovic was shown a straight red for aiming a stamp at Andres Guardado.
The sending off means Ibrahimovic will miss the return leg along with defensive midfielder Marco Verratti, who picked his third yelloe card of the campaign.