The striker, making his second appearance since rejoining the club, only played 29 minutes during Sunday's friendly in Budapest before being substituted with an ankle injury.
Without the Ivorian, Chelsea went to beat their Hungarian opponents 2-1 thanks to goals from midfield duo Ramires and Cesc Fabregas.
Chelsea begin their league campaign with a trip to Burnley next Monday, but Drogba has suggested he may not be available as he awaits further news on his injury.
"I twisted my ankle and I couldn't continue," he told the club's official website.
"In the next few days we are going to do some treatment and I hope everything will be better."
Drogba made a sensational return to Stamford Bridge last month after being released from his contract at Turkish club Galatasaray.
During his first spell in England the Ivorian scored 157 goals in 341 appearances and collected three Premier League titles, four FA Cups and two League Cups.
