Maribor canceled out Celtic's early goal, and the sides head level into the second leg of the Champions League playoff.
The Scottish champion only is participating in the playoff round after it was reinstated by UEFA following Legia Warsaw's sanction for fielding an ineligible player at the third qualifying stage.
And Ronny Deila's men will be satisfied with a draw against Slovenian champions Maribor.
As in the first leg against Warsaw, McGregor gave Celtic an early lead, stabbing home a loose ball after Jasmin Handanovic had parried Jo Inge Berget's initial effort.
McGregor's strike arrived in the sixth minute, but Celtic's advantage was wiped out before the quarter-hour mark as Damjan Bohar slotted home.