The Spain forward - who arrived at Chelsea from Atletico Madrid for a reported £32 million fee in July - has quickly settled to life in England.
Costa has scored in both of Chelsea's Premier League wins this term while his pre-season form was also encouraging.
But the 25-year-old could miss his side's visit to Goodison Park after a Chelsea spokesman confirmed to Perform that he was suffering from a "minor muscular injury".
Chelsea added that the situation would be closely monitored in the coming days.
The news will come as a blow to Jose Mourinho as he looks to guide Chelsea to a rare win at Everton.
The Merseyside club have won four of the last five league matches between the two sides at the venue. Ex-Chelsea striker Samuel Eto'o is in line for his Everton debut in Saturday's match.
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