Messi suffered the injury in Barca's 4-2 win over Sevilla in Saturday's top-of-the-table La Liga clash.
Discussing five-time Ballon d'Or winner Messi on Monday, Bartomeu said: "Messi will be out for however long he needs to be.
"Without Leo we are still competitive, but the important thing is to move forward.
"We have to win, of course, and prepare ourselves. The players are conscious of where they are."
Bartomeu's message was matched by Gerard Pique, who said he believes that the club has enough cover to cope with the Argentine's absence.
Ernesto Valverde is likely to call on Ousmane Dembele or Malcolm to replace Messi during his absence, while Luis Suarez and Philippe Coutinho will face greater responsibilities in the attack.
Malcolm has featured twice in the league since making the move from Bordeaux over the summer while Dembele has scored three goals in nine matches this campaign.
Messi has scored seven La Liga goals for the Spanish champions this season and 12 in all competitions.
Barca will host Champions League rivals Inter at Camp Nou on Wednesday before entertaining Madrid in La Liga on Sunday.