David Vallenilla's 22-year-old son, also called David, was shot by military police on Thursday.
Mr Vallenilla says he once worked with the president on Caracas' transport system, and called on his "former colleague" to clear his son's name.
The president has said firearms must not be used on protesters.
"I want to speak to my former colleague of the Caracas Metro," Mr Vallenilla told a group of reporters outside the morgue.
"Nicolás Maduro, you know that we worked together, I'm Supervisor Vallenilla."
He said he used to be Mr Maduro's boss, although the past working relationship between them has not yet been confirmed.
President Maduro is a former bus driver, who got involved in trade unions and then national politics, becoming president in 2013 after his predecessor Hugo Chavez died.
"Please, Nicolás, my friend," Mr Vallenilla said with tears streaming down his face, before calling on the leader to make it clear that his only son "was not a criminal, he was a graduating student".
"You met him when he was little," he added.
Earlier in the week, Fabián Urbina, 17, was also shot and killed as security forces and demonstrators clashed in Caracas.
There have been almost daily anti-government protests in Venezuela for over two months as the country's economic and political crisis has worsened.
More than 70 people have been killed in protest-related violence since 1 April, according to figures released by the chief prosecutor's office.
On Thursday, Interior Minister Néstor Reverol tweeted to confirm the death of a protester and said a police sergeant had fired an "unauthorised weapon".
President Maduro, in a press conference on the same day, said: "I am giving the clear order that you can not use firearms. I am giving the clear order that you can never shoot in a demonstration, under any conditions."
A group of demonstrators returned on Friday to the place where Mr Vallenilla was killed, and set some trucks on fire.
Also on Friday, supporters of jailed opposition leader Leopoldo López released footage that they say captures his cries from a military prison on the outskirts of Caracas.
"Lilian!" he calls to his wife. "They are torturing me!"
In a press conference earlier the same day, Lilian Tintori said she has not been able to see him for 19 days and his lawyers have been denied access for 78 days.
News site Ultimas Noticias has responded by publishing photos of the politician, which they say are from Friday and show him to be "fine".
López is three years into a 14-year sentence for inciting violence during anti-government protests in 2014.
A man whose son was killed during an opposition protest in Venezuela's capital Caracas has made a personal plea to President Nicolás Maduro.