The incident occurred towards the end of normal time in the cup quarter-final encounter in the Chechen capital as a large number of Zenit fans took off their tops.
That incited anger among home fans in the majority-Muslim city, who were seen leaving their seats en masse and charging towards the away sector.
Direct violence appeared to be averted only by the actions of quick-thinking stewards, who raced to form a barrier between the two sets of supporters to keep the peace.
Akhmat’s Oleg Ivanov and Zenit’s Grozny-born midfielder Magomed Ozdoev were reportedly among the players who urged fans not to let the unrest spiral out of control.
The game was held up as the tempers were eventually quelled, before Zenit went on to claim a 2-1 win in extra time thanks to a strike from veteran former Chelsea star Yuri Zhirkov.
As in many leagues elsewhere around the world, exposed male torsos are not an uncommon sight in Russian football, particularly towards the end of matches.
However, in response to the scenes in Grozny, the Zenit press service issued a reminder for fans to “always respect each other’s traditions.”
Zenit manager Sergei Semak said: “Of course traditions should be honored and respected. As for our fans, this is their habit. Not everyone understood everything correctly.
“We need to talk and find a compromise. Our fans travel everywhere. I understand that here their behavior was seen in a different way.
“It’s difficult to say if they knew about local traditions or not. We’ll speak with the fans. In any case, any conflict needs to be resolved peacefully and we should always respect each other… No one liked what happened.”
Russian Premier Liga leaders Zenit will meet Spartak Moscow in the semi-final, after Spartak secured a 3-2 derby win against CSKA in a titanic tussle in the Russian capital.
The game was settled by an extra-time strike from Jordan Larsson, son of former Celtic and Barcelona star Henrik.