Aeroméxico, Air Canada, Alitalia, Latam, Lufthansa and United Airlines have already stopped their flights.
Avianca, which has operated in Venezuela for 60 years, says the move comes into effect on 16 August.
The airline, one of the biggest in Latin America, said customers who had bought tickets for flights departing after that date would be reimbursed fully.
Airlines still operating flights to Venezuela include Air France, Iberia, Air Europa and TAP, but Venezuelans have complained about the increasing difficulty of getting flights in and out of the country.
Many used Avianca's twice-daily Caracas to Bogotá route to connect with other flights.
With fewer flights available those having to book at short notice sometimes struggle to get seats.
The Venezuelan women's volleyball team missed the world grand prix tournament in Canberra, Australia, on the weekend.
The team had to use chartered planes because a shortage of seats stopped them taking commercial flights to Australia, Venezuela's chargé d'affaires Daniel Gasparri-Rey said.
But when the chartered planes were delayed and it became clear the team would arrive too late to take part in the tournament, they turned back, the diplomat said.
The Venezuelan Volleyball Federation could now face a fine of up to $30,000 (£23,800) for missing the matches.
Player María José Pérez said the team members felt "frustrated" because they had been robbed of the chance to make an impression at the tournament, for which they had qualified for the first time.
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