No one was hurt in the blast at the home of Cardinal Julio Terrazas and there was only minor damage, CNN said, citing Bolivian media reports.
Terrazas, 73, wasn't at the residence at the time.
CNN said the church has been a target in the past of harsh criticism from Bolivian President Evo Morales, who Tuesday won approval from the National Congress to run for re-election. Morales has accused the church of blocking reforms.
NBC reportedly holds celebs hostage to Jimmy Fallon's show
Aaron Carter is still in love with Hilary Duff