The Croatian and fellow striker Alvaro Morata were substituted towards the end of Juve’s 0-2 win away to Genoa on Sunday.
Subsequent scans “revealed a first grade tear in his right thigh muscle”.
“He will be sidelined from competition for 20 days,” a statement on the Italian champions’ website read.
It means the former Atletico Madrid forward will miss the UEFA Champions League Match Day 2 encounter between the last season finalists and reigning Europa League champions Sevilla in Turin on Wednesday, 30 September, 2015.
Mandzukic could also miss his country’s crucial UEFA EURO 2016 qualifier against Bulgaria on 8 October.
Juve has positive news from tests conducted on Morata, who complained of abdominal pain on Sunday, disclosing that there is no strain or tear.
Juventus are in Sere A action at home to Frosinone on Wednesday.