Messi, the world player of the year, scored the opening goal against Almeria on Saturday night, but was forced to leave the pitch soon afterwards with a hamstring problem in his right leg.
"Leo Messi has a small injury to the biceps femoris (thigh) in his right leg," a Barcelona statement read.
"The Argentinian will be out for approximately two to three weeks, which will certainly force him to miss Barcelona's two games this week - on Tuesday against Celtic and next Saturday at the Camp Nou against Valladolid."
The 2-0 win at Almeria made it seven wins out of seven in La Liga for Barca, setting a club record for the best start to a Spanish league campaign.
Messi joins a growing injury list for the Spaniards; Javier Mascherano and Jordi Alba are both out with hamstring problems while veteran centre-back Carles Puyol is another who will not feature at Celtic Park.
Barcelona opened their Group H Champions League campaign with a 4-0 home win over Ajax while Celtic were going down 2-0 in Milan.