President Nicolas Maduro is accused of controlling the court, which has fended off numerous legal and legislative moves against him over the past year and a half.
Attorney General Luisa Ortega, a staunch ruling party figure, is the highest public official to defy Maduro in the current standoff.
Last week she filed a challenge against his effort to rewrite the constitution, branding it undemocratic.
On Monday the court said on Twitter that it was dismissing the appeal since it was presented in an "incompetent" way, grouping together separate complaints against various different state bodies.
Opposition lawmakers also filed other court cases on Friday against Maduro's constitutional plan.
Clashes at daily protests by demonstrators calling for Maduro to quit have left 66 people dead since April 1, prosecutors say.
Protesters blame Maduro for an economic crisis that has caused desperate shortages of food and medicine in the oil-rich country.
Maduro says the crisis is a US-backed conspiracy.
He has launched moves to reform the constitution in response to the protests, but his opponents say that is a ploy to cling to power.
The president retains the public backing of the military. However, its commander Vladimir Padrino Lopez sounded a moderate note last week when he warned security forces against attacking protesters.
Analysts said last week that Ortega's suit could build bridges between the opposition and disgruntled officials and widen divisions in Maduro's camp, making it harder for him to stay in power.
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