CARACAS, Venezuela—President Nicolás Maduro took over the last independent institution in Venezuela on Sunday when his allies replaced the opposition head of the National Assembly, Juan Guaidó, with their own lawmaker in a maneuver that was condemned from Washington to Latin America.

Mr. Guaidó and other congressmen that form the assembly’s opposition majority were barred from entering as Mr. Maduro’s allies in the body and some new converts who had previously opposed the regime chose Luis Parra as the new president. The machinations...