Both players hobbled out of the 0-0 Serie A draw with Fiorentina on Saturday, Costa managing only eight minutes and Pjanic forced to depart shortly before half-time.
The Bosnia-Herzegovina midfielder had tests at J Medical 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 Thursday (AEST).
However, Costa has been diagnosed with a thigh injury and it will be 15 days before a definitive time frame on his recovery can be put in place.
It means the Brazil winger will sit out the Atletico clash and potentially Juve's second Group D match at home to Bayer Leverkusen on 2 October (AEST).
He will also miss league matches against Hellas Verona, Brescia and SPAL over the coming 10 days.