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7 year oldFabián Urbina, 17, was shot as security forces and demonstrators clashed in the Altamira neighbourhood.
Interior Minister Néstor Reverol spoke of a possible "improper and disproportionate use of force" by the security forces.
He said that a number of officers were being investigated.
Mr Reverol also condemned "the violence and the calls for an uprising made by the Venezuelan opposition".
Rights ombudsman Tarek William Saab tweeted [in Spanish] that two members of the National Guard had been detained over the "undue use of a firearm".
There have been almost daily anti-government protests in Venezuela for the past 80 days as the country's economic and political crisis has worsened.
Many of the marches have ended in violence as protesters threw petrol bombs and stones and police fired tear gas.
More than 70 people have been killed in protest-related violence since 1 April, according to figures released by the chief prosecutor's office.
A list published by the information ministry puts that number higher and suggests most of those killed were taking part in anti-government demonstrations.
But among the dead are also members of the security forces, people caught up in the violence, and a group of men who were electrocuted when a bakery was looted.
Monday's opposition march was called to denounce government plans to convene a citizens' assembly to draw up a new constitution.
Opposition activists say the constituent assembly is an attempt by President Nicolás Maduro to consolidate his power and bypass the opposition-controlled National Assembly.
The president argues that the aim of the new constitution is to safeguard social programmes created by his socialist government and that of his predecessor in office, Hugo Chávez.
While anti-government protesters clashed with the security forces in Altamira, supporters of the government took part in a "anti-imperialist march in support of the constituent assembly" in the city centre.
The aim of that march was to send a message to members of the Organization of American States (OAS) meeting in Mexico not to interfere in Venezuelan affairs.
Foreign ministers of OAS member states have again discussed the political and economic crisis in Venezuela, but failed to agree on a resolution criticising the Venezuelan government.
The draft resolution which called on President Maduro to drop his plans for the constitutional assembly was backed by 20 countries, opposed by five and eight abstained.
Twenty-three votes were needed to adopt the resolution.
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