Official said the captain was shot late on Sunday at a street barricade set up by demonstrators.
Venezuelan President Nicolas Maduro has offered asylum to former the US intelligence contractor.
The Venezuelan opposition leader has been charged with inciting post-election violence.
Nicolas Maduro narrowly beat opposition challenger Henrique Capriles in the polls.
The Venezuelan acting president pledges to rule out corruption after accusations by election rival.
Venezuela’s opposition leader joins election race vowing to challenge Chavez’s preferred successor.