Anne Arundel County Fire Department Battalion Chief Steve Thompson said the car dropped about 40 feet into about 6-8 feet of water, The Baltimore Sun reported. He said the 22-year-old driver made her way out of the vehicle and over to nearby rocks.
A boater reached the unidentified woman and stayed with her until paramedics arrived in a fire department boat to transport her, the newspaper said.
Thompson said the woman was hospitalized in critical condition but her injuries appeared to be non-life-threatening, the Sun said.
The car went over the railing near the eastbound start of the span, transportation and fire officials told the newspaper.
The crash prompted authorities to close the eastbound lanes of the bridge and divert traffic to the westbound lanes, Maryland Transportation Authority spokeswoman Kelly Melhem said. The bridge would not be reopened before engineers inspect it for damage, she said.