Tests had confirmed both France defender Abidal and Ivory Coast midfielder Toure had the virus and they were being treated in isolation by medical staff, the league leaders said on their website.
"We'll get through this," coach Pep Guardiola said at a news conference.
"We knew that a lot of people have it and we were at risk," he added. "Now it has arrived here and we have to make sure it doesn't spread which is why we have isolated them."
The World Health Organisation (WHO) said on Friday H1N1 flu was moving eastwards across Europe and Asia after appearing to peak in parts of western Europe and the United States.
At least 6,770 deaths have been recorded worldwide since the virus, known as swine flu, emerged in April, according to the latest WHO update.
Five players from Barca's league rivals Osasuna have contracted swine flu in recent weeks and a second-division match involving Real Betis had to be postponed last month after 13 players from the squad were hit by the virus.
Atletico Madrid coach Quique Sanchez Flores was unable to take training earlier this week after falling victim but had recovered sufficiently by Friday to return to work.
"There's never a good time for something like this to happen," Guardiola said. "It's true we have important matches coming up but with the others we will get by."
