A club statement said that the 36-goal hitman, who has been a key element in Atletico's La Liga title-winning side, had suffered a "grade one muscular injury" to his thigh in the final match of the season against Barcelona at the weekend.
It is the third time in recent months that Costa has had problems with his thigh but this is the first occasion where it is a tear rather than a strain.
Although it means he is now unlikely to be ready to face Real Madrid in the final in Lisbon on Saturday, Simeone remains positive.
"There are several days to go and we are not going to predict now, so soon before such an important match. He is an important player but he needs to be ready," Simeone told a news conference on Monday.
Atletico, who clinched the league title with a 1-1 draw at Barcelona on Saturday, are in the final stages of a historic season but the intensity of the campaign has taken its toll and Arda Turan is also a doubt for the final with a pelvic injury.
"We will wait to see how Arda and Costa are by the end of the week. Given the situation that they are not ready then we will look for alternatives," said Simeone.
The Argentine said that the team are now fully concentrated on the final with Real after their league triumph.
"It is always better to win and improve the morale of the players and the people. While we have celebrated we have to now turn the page and we have several days to work hard knowing that we will face strong rivals," said Simeone.
"I would say that we have a 50 percent chance in the game. They have better individual players but we are a team. We have plenty of motivation and they will have plenty as well which means that it will be an equal match with the key in the middle of the pitch."
Atletico have met Real on four occasions this season with a win and a draw in the league but they lost both legs of their King's Cup semi-final tie.
"The final will be different, I don't see similarities with the other matches. It will be a game with friction and anxiety. Whoever is able to put to one side the importance of the match will be in best conditions to win," said Simeone.
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