Roux was called before a French Football Federation (FFF) disciplinary commission after the incident during a clash with Mons on July 20.
There were fears he could be banned for anywhere up to nine months if he was found to have deliberately spat at the Belgian official, Nicolas Laforge, after he was denied a free-kick.
That would have effectively ended his Ligue 1 campaign before it began but he will now miss only the early-season games against Lorient, Reims and St Etienne, while his club were ordered to pay a 1,000 euro fine.
Lille general director Frederic Paquet told L'Equipe after Roux's hearing: "Nolan explained once again his version of events. This was set against that of the referee and we showed quite convincing pictures which confirm Nolan's version.
"In his head, at no time did he want to provoke the referee. He explained that today in a very clear and composed manner."
Once the verdict was released, Paquet added on the club's website: "LOSC take note of the FFF's decision and will wait to hear the explanation of what led it to impose this sanction."
Roux, 25, scored eight goals in 32 league games for the club last season.