Both players were taken off hurt during Barca's 3-0 Copa del Rey semi-final win over Atletico Madrid on Tuesday, with the Catalans ousted 4-3 on aggregate.
"The time of the recovery process (for Balde) will be four weeks," said Barcelona in a statement, without specifying how long Kounde will miss.
Spanish media reported that France international Kounde, 27, is likely to be sidelined for a similar length of time.
As well as the Champions League matches, the duo will also miss LaLiga games against Athletic Bilbao, Sevilla and Rayo Vallecano.
Barcelona are currently also without midfielder Frenkie de Jong, who also has a hamstring injury.
The injury makes Kounde a doubt for France's friendlies against Brazil and Colombia in the United States at the end of March, in the build-up to this summer's World Cup.
Balde is a Spain international but has been behind Marc Cucurella and Alex Grimaldo in coach Luis de la Fuente's pecking order.