The Jewish community in Venezuela has denounced the attack by the state media on Henrique Capriles.
An article published on the Venezuelan State Radio website entitled The Enemy is Zionism criticised Mr Capriles's Jewish ancestry.
Efraim Lapscher, vice-president of the Venezuelan Confederation of Israelite Associations, the country's main Jewish umbrella group, said the piece was "clearly anti-Jewish" and accused the government of both "demonising Zionism" and using antisemitism as a "political tool".
"There are clearly people inside the Chávez government who cannot hide their antisemitism," Mr Lapscher said. "But a xenophobic campaign against Capriles is destined to fail."
Mr Lapscher says his organisation is growing increasingly disheartened by the government's use of state media to attack the Venezuelan Jewish community.
Venezuela National Radio also broadcast antisemitic comments last April, while Mr Lapscher suggested the government may have been behind an attack on Caracas's main synagogue in 2009. Government officials did not comment on the claims.
Colette Capriles, a political analyst at the Simón Bolívar University in Caracas, called the slurs on Mr Capriles's character "absurd and disproportionate" and part of a "dirty campaign".
"It's a grave error by the government and it's actually helped Capriles," she said.
"Chávez's alignment with extremist Islam is damaging," said Ms Capriles. "I think Capriles would be more prudent internationally."