The murder was denounced by the head of the governing body, Delcy Rodriguez.
The dead lawmaker was identified as Tomas Lucena, a member of the assembly for the western state of Trujillo.
Rodriguez said those responsible for the crime "will be punished" though she did not specify the circumstances nor the motives of the killing.
"Nothing will stop the Constituent Assembly and its defense of Venezuela," Rodriguez said, suggesting however that the motive may have been political.
The Constituent Assembly was set up last year by President Nicolas Maduro at the height of an opposition campaign to depose him, with the aim of usurping the power of the opposition-dominated National Assembly.
Trujillo governor Henry Rangel said he had received Maduro's "full support" to clarify the facts of the killing.
"We will not allow this crime to go unpunished," Rangel wrote on Twitter.
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