The Maryhill outfit claim a “shower of objects” rained down on the home dugout from the Colin Weir Stand during the second half of the cup tie, with some landing between the former Hibs defender and Hearts boss Craig Levein.
The Daily Record is reporting that two flash-points sparked the incidents - Uche Ikpeazu’s penalty shout and Christie Elliott’s 72nd-minute equaliser.
More than 2500 Hearts supporters packed out the Colin Weir Stand for the crucial last-eight tie, which finished 1-1. The tie will be replayed on Tuesday, March 12.
The Jags are understood to be deciding what action to take. Club chairman Jacqui Low met with chief executive Gerry Britton earlier this week to discuss the incidents.
A spokesperson for the Ladbrokes Championship side told the Record that the club was investigating a “number of incidents” from Monday night’s televised clash.
The source said: “What has concerned us the most is the number of coins that were being thrown. It wasn’t isolated stuff - they were coming down in showers around the dugout and technical area. We’re just relieved that no-one was hurt.”
The incident is the latest in a long line of disorderly conduct from Scottish football fans.
Celtic manager Neil Lennon was struck by a coin at an Edinburgh derby thrown from the Main Stand at Tynecastle last Hallowe’en during his time as Hibs head coach, and in the same match Jambos keeper Zdenek Zlamal was assaulted by a fan in the Roseburn Stand.
Earlier this season, assistant referee Calum Spence needed treatment after suffering a gashed head when a coin was thrown by a Rangers fan during a league clash against Livingston at Almondvale.
Light Blues forward Alfredo Morelos was targeted by thugs who threw a coin at him at St Mirren’s Simple Digital Arena and Kilmarnock striker Kris Boyd was also hit by a coin during Celtic’s 1-0 win at Rugby Park last month.
This past weekend, seats were thrown by fans at Aberdeen’s Scottish Cup clash with Rangers at Pittodrie, while there were two separate reports of bottles being thrown on to the field of play during Hibs’ clash with Celtic, one of which narrowly missed Hoops player Scott Sinclair.
PFA Scotland demanded last week that action be taken before one of their members is “maimed” during a match.