Colombia’s drawn-out investigation into a continent-wide bribery scheme by Brazilian construction giant Odebrecht SA is casting a shadow over the nation’s biggest banking group, owned by one of Latin America’s richest men.

Grupo Aval Acciones y Valores SA and a subsidiary have seen their shares underperform since Odebrecht admitted to one of the largest graft cases in corporate history, detonating scandals across Latin America. One of Aval’s companies, Corficolombiana, partnered with Odebrecht on its biggest Colombia project: a section of the $2.5 billion highway known as Ruta del Sol. Odebrecht paid millions in bribes to win the contract, while Aval...