"I ask each of you, every manager, every soldier, every supporter, not to turn to violence and to make every effort to restore the calm and responsible democracy that our nation is waiting for," Drogba, spokesman for the national soccer team, was quoted as saying in a statement in French daily Le Figaro.
Drogba urged the international community to be measured in its response to the dispute, saying Ivorians would suffer if the country is deprived of funding from international lenders like the IMF.
The World Bank said on Wednesday it had frozen funding to Ivory Coast as incumbent president Laurent Gbagbo resists mounting international pressure to relinquish his post.
World powers and African states have backed rival presidential claimant Alassane Ouattara, and fears are growing that the standoff could tip the West African country back into civil war. The 2002-3 conflict split Ivory Coast in two.
Drogba, who also plays for English Premier League champions Chelsea and is a UNDP goodwill ambassador, is an idol in Ivory Coast, embodying a dream of a route to glamour, wealth and fame.
He and his team, known as the Elephants, played an important role in convincing rival fighters to lay down arms and negotiate in 2006 when Ivory Coast qualified for its first World Cup.
Nearly 200 people have been killed since the contested November 28 election, according to the United States.
"We hope that a solution will soon be found to avoid any confrontation on the street," said Drogba, who took no particular side in his statement.
Drogba was named as one of Time magazine’s 100 most influential people earlier this year in part for his charity work which includes a foundation to provide financial and material support for health and education across Africa.