Prisons official Iris Varela says inmates at La Planta prison in Caracas had dug the tunnel leading to a sewer pipe that emerges alongside a river.
Varela said authorities had been investigating the possibility of an escape attempt for three days, and that on Friday firefighters spotted the tunnel while carrying out an inspection. She said that after the tunnel was discovered, officials installed bars in the sewers.
She said it was unlikely any prisoners had managed to escape before the tunnel was found.
Venezuela's overburdened prisons were built to hold about 12,000 inmates, but officials have said the prisons now hold about 47,000.