"I ask for the forgiveness of all those hurt by my act. In particular, I ask the faithful of the Warsaw diocese to forgive me for having betrayed their trust," Monsignor Piotr Jarecki said in a statement in which he acknowledged having driven while intoxicated.
The 57-year auxiliary bishop of Warsaw was detained briefly on Saturday after running his car off the road.
Police said he had a level of 2.5 grammes of alcohol per litre of blood. Poland's limit is 0.2 grammes, and driving while intoxicated can carry a penalty of two years in prison.
Jarecki was set free after his blood test and ordered to return to a police station next week.
"That's the point at which he's likely to be charged with driving under the influence," police spokesman Mariusz Mrozek was quoting as saying by Poland's PAP news agency.
Jarecki pledged to take a course of therapy to cure his drink problem and that he had placed his professional fate in the hands of Pope Benedict XVI.
The Church has a high-profile role in Poland, where the vast majority of the country's 38 million people is Roman Catholic.