The 36-year-old, back at Stamford Bridge following a two-season absence, was assessed on the Blues' return to London after going off during the first half of Sunday's friendly win over Ferencvaros in Budapest.
Neither manager Jose Mourinho or Drogba himself appeared too concerned after the match and it is understood the results were positive and a lengthy absence is unlikely.
Drogba said: "I twisted my ankle and I couldn't continue.
"In the next few days we are going to do some treatment and I hope everything will be better."
Drogba could be available for Monday's first Premier League clash at Burnley, but he is likely to begin the season as second or third-choice striker.
Diego Costa, the new signing from Atletico Madrid, is Mourinho's first choice, with Fernando Torres also an option up front.
Samuel Eto'o, Demba Ba and Romelu Lukaku all left Chelsea this summer.
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