Two collared peccaries, a mammal similar to a pig, went missing over the weekend from the Zulia Metropolitan Zoological Park, near Venezuela’s northeastern border with Colombia.
“What we presume is that they (were taken) with the intention of eating them,” said a local police official.
An economic crisis gripping socialist-run Venezuela has left many supermarket shelves empty.
A recent study revealed 93% of Venezuelans cannot afford to buy enough food and 73% have lost weight in the last year.
But the zoo’s chief Leonardo Nunez denied the thefts were related to food shortages.
He claimed drug dealers seeking to sell animals were behind a recent crime wave affecting 10 species of animal, including a buffalo he said was cut into pieces.
“They take everything here. The animals weren’t stolen to be eaten,” said Mr Nunez.
Former zoo director Mauricio Castillo said thieves had made off with two tapirs – another mammal similar to a pig that is classed as vulnerable to extinction.
Venezuela’s president Nicholas Maduro has blamed the country’s food shortages on an “economic war” waged by right-wing opponents and the US.
The shortages have left zookeepers unable to properly feed their animals, with some 50 estimated to have died within six months last year at one of the country’s main zoos in the capital Caracas.
The government denied the animals had starved.
This year, more than 100 people have been killed in four months of anti-government protests in Venezuela, with hundreds more in prison, to bring international condemnation of Mr Maduro’s regime.
Critics have claimed the country, which has the world’s largest reserves of crude oil, is heading towards dictatorship after the recent election of a new legislative body to redraft Venezuela’s constitution, following a “sham” vote.
Two leading government critics, Leopoldo Lopez and Antonio Ledezma, were jailed in the wake of the vote.
Earlier this month, US President Donald Trump revealed he would not rule out a “military option” amid Venezuela’s political crisis, having already imposed sanctions on Mr Maduro.