The Sept. 16-18 match will be held in Lima instead of Barcelona, Venezuela, the federation said in an emailed response to a Reuters inquiry.
"We're surprised because we have never had negative comments about security," Luis Contreras, president of the Venezuelan Tennis Federation, said at a press conference. "It's an unfair decision from every point of view."
Government officials have said security problems have been exaggerated by the media.
Venezuela has one of the world's highest violent crime rates and has been rocked by political protests as opposition groups seek a recall referendum on the rule of President Nicolas Maduro.
"Now the ITF is a political and economic organisation? Why not suspend the Cup in France, which has suffered two attacks? Why is it suspended in Venezuela?" Eduardo Alvarez, president of the Venezuelan Olympic Committee, said at the press conference.
Alvarez had suggested the match should take place in Cuba, an ally of Venezuela's socialist government.
Delegations of athletes who have travelled to Venezuela to compete in international cups or the World Cup qualifiers have had to bring their own medicines and toiletries because of shortages in Venezuela as the country grapples with an economic crisis.
(Additional reporting by Brian Ellsworth; Writing by Brian Ellsworth; Editing by Andrew Hay and Richard Chang)
