Vaslui defender Zhivko Milanov lost five teeth after being kicked by Cadu, Cluj's captain, who mistimed a challenge for a loose ball during Monday's goalless draw.
Cadu, 31, who joined the Romanian champions from Portuguese side Boavista in 2006, has helped The Railwaymen to win three league titles and three national cups in the last five years.
"It's a blow for CFR," Cluj president Iuliu Muresan told local media after the ruling by the Romanian professional league. "This decision is not normal, it's an unfortunate accident. It's clear that we'll appeal against the punishment."
Cadu, who was also fined 18,000 lei, apologised to Milanov and said he had not meant to hurt him.
"I just wanted to hit the ball and he had his head too low," the Portuguese, who was sent off after the incident, said. "I didn't see him and I didn't mean to hit him. I just couldn't stop. Once I hit him I realised what happened. Sorry!"
Cluj, who finished third in their Champions League group behind Manchester United and Galatasaray this season, are sixth in the standings with 33 points from 20 matches, 17 points behind leaders Steaua Bucharest.