Remi Garde's side secured a 2-1 win at their local rivals, with winger Jimmy Briand heading home the winner in the third minute of injury time after Saint-Etienne's Romain Hamouma had cancelled out Alexandre Lacazette's opener.
Aulas says he was struck by Ruffier during unsavoury scenes after the final whistle.
"One of our doctors made a remark on his way back to the dressing-rooms. Fabrice Grange, the Saint-Etienne goalkeeping coach, a former Lyon player and France international, thought it was a good idea to hit our doctor," Aulas told Canal+.
"While I was trying to separate them, Stephane Ruffier gave me a big blow on the back."
However, Ruffier denies the allegations, he told Le Parisien: " He said I hit him in the back, this is outrageous! If I did, he could not do an interview with Canal + three minutes later ...
"I do not attack people in the back, and anyway, I wouldn't attack anyone, it is not my education . [...] His statements are shameful."
The Rhone derby is one of the fiercest rivalries in French football and tensions were increased when local authorities opted to ban Lyon fans from the Stade Geoffroy-Guichard following violent clashes between the two sets of supporters last season.
Controversy dominated the build-up to the game as Saint-Etienne fans attempted to confront Lyon goalkeeping coach Joel Bats after he tied a club scarf to one of the nets.
And Aulas was quick to condemn the home followers for their actions.
"I watched all the hubbub in the stands from the start of the game," he added.
"Their supporters threw toilet paper at our goalkeeper. The officials didn't see the reality.
"Luckily, it turned out well for us. What happened on the pitch is incredible. Some idiots managed to get onto the pitch after Joel Bats put one of our scarves in the goal.
"All of that is a shame as football is a party. With regard to Joel Bats, he was completely right to tie that scarf on. The supporters, who couldn't watch the derby, deserved it."