The right back was substituted in the 65th minute of Atletico's 0-0 home draw with Real Betis in La Liga on Sunday and was replaced by Sime Vrsaljko, who will likely line up on the right of the defence against the Gunners.
"Juanfran took tests which determined that our full back suffered an injury to the hamstring in his left leg," said Atletico in a statement on Monday.
No recovery time was stated but reports in Spain indicate he will be aiming to recover in time for a potential final, should Diego Simeone's side progress.
Former Chelsea striker Diego Costa is also unlikely to be fit for Thursday's first leg in London after suffering a hamstring injury earlier in April.
"I think he has little chance of playing on Thursday in the first leg, but he will be back for the second," said Simeone.
(Reporting by Rik Sharma; Editing by Christian Radnedge)
