Messi, who missed training ahead of the match against Lille, was replaced by Mauro Icardi. The former Barcelona forward has yet to score a Ligue 1 goal after moving to PSG in the summer.
"We hope that [Messi's] evolution will be good and that he can be with us as quickly as possible. I cannot say anything more," PSG manager Mauricio Pochettino told reporters.
"[Mbappe] always has a good motivation and the desire to help the team. He works very well."
Teammate Mbappe, however, who had to sit out the Lille game with an infection, was included in PSG's Champions League squad.
The French club are top of Group A with seven points from three games, with Manchester City second on six. Club Brugge are on four while Leipzig have yet to earn a point after losing all three games so far.
With Messi out, his Argentina teammate Angel Di Maria will get a chance to play his first Champions League game of the season.
Di Maria, 33, was PSG's standout performer against Lille in Mbappe's absence, providing the assist for the equaliser before scoring the winner two minutes from fulltime.
"All the players are important but some shine on their own. Angel brings balance to the team, he brings his experience," Pochettino added.
"He's been here for six years, he's very important. We can always count on players like him.
"Teams need balance, this ability of all players to invest in all phases of the game. The collective remains the most important. If this works perfectly, the individualities will appear in a natural way -- we continue to work on this balance."