McGregor handed Celtic the lead three minutes into the game on his first appearance in more than two months.
The goal raised the noise levels in Celtic Park and Leigh Griffiths fired a shot into the arms of Jasper Cillessen after seven minutes.
Ajax then thought they had pulled a goal back, but Viktor Fischer was adjudged to have strayed offside, although replays suggested otherwise.
Lasse Schone tested Craig Gordon with a fierce strike from a narrow angle and the Celtic goalkeeper denied Fischer a few moments later, but he was helpless to prevent Milik from prodding home the loose ball.
Griffiths and Younes each had two more chances in the latter stages of the first half, but neither could force the ball home as the sides went in at the break all square.