The Brazil-born Spaniard has missed Chelsea's last three matches - including Sunday's draw with Manchester United - with an injury aggravated on international duty
Costa has been sidelined since featuring twice for his country in Euro 2016 qualifiers against Slovakia and Luxembourg, suffering from muscular problems and a virus.
Mourinho says the latter issue has now cleared up but insists his lingering problems were caused by his international commitments.
"The virus is fine," the Portuguese told reporters. "It was hard, he had to go to the hospital and obviously it doesn't help him to recover from his injury. But he didn't play on Sunday because of the injury, not because of the virus.
"Diego has the hamstring [injury] because he played two matches in three days when he was not with us."
Questioned whether he hoped Costa's fitness problems were over, Mourinho quipped: "But he still has [to play for] the national team in November!"
Chelsea face League Two outfit Shrewsbury Town in the League Cup on Tuesday, with Costa unlikely to feature, but Mourinho insists he is not taking the fourth-round fixture lightly.
"You can say that Shrewsbury in the League Cup is a friendly, but we have to play the match and respect the match," Mourinho added.
"They are doing very well in their league, they did very well against superior teams [Norwich City, Blackpool and Leicester City] in the League Cup.
"It is a big day for them and we know it is going to be difficult for us. And because we have so many injured players, it is even more difficult."