Alka Himanshu Tanna, of Silver Spring, Maryland, was coming out of the bank on New Hampshire Avenue around noon and was crossing a parking lot when she was hit by an oncoming vehicle, the Montgomery County Police Department said.
The car was a white Lexus being driven by her husband, identified as Himanshu Maganlal Tanna, the agency said.
The 59-year-old accelerated and struck his wife several times, police said. He then crashed into a nearby lamp post after knocking down a front column outside the bank.
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No one else was in the car during the deadly incident. When officers arrived at the scene, Tanna provided a statement and was taken into custody, police said.
He has been charged with first-degree murder and is being held without bond.
A motive for the alleged killing has not been determined.