The Bosnia-Herzegovina midfielder had tests at the club’s medical centre on Monday and no muscle damage was detected, meaning he should be clear to play in his side's Champions League group-stage opener away to Atletico on Wednesday.
However, Costa has been diagnosed with a hamstring injury and it will be 15 days before a definitive time frame on his recovery can be put in place.
He will also miss league matches against Hellas Verona, Brescia and SPAL over the coming 10 days.
The duo have started all three of Juventus’ matches this season meaning boss Maurizio Sarri will have to make at least one change to his side for the trip to Wanda Metropolitano.
Juventus, Italian champions in each of the last eight seasons, are currently third in the embryonic Serie A table after taking seven points from their opening three matches.
They travel to Madrid on Wednesday hoping this will be the season they finally end their wait for a third Champions League title.
The Bianconeri, who last won the trophy in 1996, have been runners-up on seven occasions, including twice in the last five seasons.
The off-season saw changes both on and off the pitch, with Sarri returning to Italy to replace Massimiliano Allegri in the dugout.
The 60-year-old was only able to take to Juve dugout for the first time on Saturday after overcoming a bout of pneumonia.
They also made waves in the transfer market, with the biggest deal being the €75 million (£68m/$84m) capture of Netherlands defender Matthijs de Ligt.