A security official said the officer involved was arrested after dozens of bystanders protested at the scene of the shooting in an eastern suburb of the capital, chanting: "The police are thugs."
"During a police patrol a dispute broke out between the officer and the seller over the price," the ministry said in a statement.
"The policeman opened fire, killing the vendor and wounding two passers-by."
Egypt's police have been on the defensive after rights groups denounced alleged torture and deaths in detention, as well as arbitrary arrests and the disappearances of government opponents.
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The alleged abuses are reminiscent for many Egyptians of those perpetrated by police under the rule of longtime president Hosni Mubarak, who was toppled in 2011 partly as a result of public outrage to impunity for security services.
A court this month sentenced a policeman to life in prison for shooting dead a taxi driver over a fare dispute.
President Abdel Fattah al-Sisi had said he would ask parliament to amend the law to toughen sanctions for police abuses after the February killing.
Thousands of doctors held a protest earlier this year against the police after officers allegedly assaulted two doctors in a hospital.
And several policeman have been detained for violence against prisoners and some have been sentenced to jail in the past year.