Bishop Heather Cook became Maryland's first female Episcopalian bishop after being elected a suffragan in September.
Last month she was involved in a collision with cyclist Thomas Palermo, 41, who died from his injuries. The Episcopal Church has said Bishop Cook left the scene, before returning twenty minutes later.
Prosecutors say she was three times the state's legal alcohol limit when she was tested by police.
She has been remanded in custody, and faces charges of vehicular manslaughter, leaving the scene of an accident resulting in a death, driving under the influence of alcohol, and texting while driving.
The Episcopal Church is also investigating her actions.
Mrs Cook previously pled guilty to drink driving in 2010.
Bishop of Maryland Rt Revd Eugene Taylor Sutton said: "The Diocese of Maryland is in deep pain.
"Words barely express the depth of our shock and despair...
"There are still too many questions for which there are no easy answers, and we are filled with anger, bitterness, pain and tears.
"Our thoughts and prayers remain with the Palermo family in their bereavement and for ourselves as a diocese in mourning.
"And we continue to pray for our sister Heather in this time of her tremendous grief and sorrow, knowing the Episcopal Church's 'Title IV' disciplinary process is underway to consider consequences for her actions as well as review the process that resulted in her election."