The assailant entered the branch of Corporation Bank in Soledevanahalli area between 4 to 4.15 pm, fired from his pistol injuring customer Muralidhar.
He then threatened the bank cashier to part with the money in his possession, estimated to be around Rs 10 lakh to Rs 12 lakh, police said.
Muralidhar later succumbed to his injury at a hospital, Deputy Commissioner of Police (North Division) Siddaramappa, who visited the spot, told PTI.
A hunt was on for the culprit, he said.