The fixture has a history of crowd trouble, especially in the last two decades when several fans have been killed and hundreds seriously injured in clashes between rival supporters.
"There is no place for violence in the game, what happened in the past should stay in the past and we must move on into the future," former Chelsea manager Grant told a news conference on Monday.
"Football violence was a problem in England 20 odd years ago but today people can come to watch their teams in action without any fear for their safety.
"I expect every Partizan fan to show their passion by supporting the club but no more than that because there is a code of conduct which has to be respected."
Prosinecki, who won the 1991 European Cup with Red Star as a player, added: "We all want a full house and an incident-free atmosphere on the terraces devoid of any trouble because this is a fans' game and everyone should be able to enjoy it."
The appeal came after a week littered with football violence in Serbia. It kicked off with fans of Rad Belgrade and Novi Pazar hurling rocks and flares at each during their league match in the Serbian capital on March 10.
Partizan fans pelted Grant with lighters and attacked the team's striker Lazar Markovic following their 0-0 home draw with Sloboda Sevojno the same day, which resulted in a one-match crowd ban they served in Saturday's 4-0 win over Jagodina.
Novi Pazar fans then caused trouble during Wednesday's 2-1 home defeat by Vojvodina Novi Sad.
The incidents prompted UEFA president Michel Platini to warn the Serbian Football Association during last week's two-day visit to Belgrade that the body needed to take stronger action against offenders.
CHASING RECORD
Leaders Partizan, who are six points ahead of Red Star in the league and are aiming for a record fifth successive league title as well as a second successive domestic double, will miss injured left back Aleksandar Volkov.
Red Star will be at full strength and buoyed by Saturday's 4-1 league win at neighbours BSK Borca, taking their tally to eight goals in the last two games after beating Smederevo 4-0 at home in the previous round.
"We are in good form, we have chalked up four league wins in a row and while we need to keep a clean sheet because away goals count, the imperative is to score one more goal than the opposition so we will attack from the off," said Prosinecki.
"A win would also boost our confidence ahead of the run-in for the league title but we know that the cup is our best chance to win some silverware this season."
Vojvodina Novi Sad, aiming for their first national cup after losing five finals, are away to unheralded Borac Cacak in the first leg of the other semi-final.
Their coach Dejan Vukicevic said the club needed to pounce on the opportunity to lift the trophy on home turf, with the final being played in Vojvodina's Karadjordje stadium in May.
"There will be no excuse if we d
