A 25-year-old man has been charged with assault after an assistant referee was attacked during the Hearts-Hibs match on Wednesday.
Hibs manager Neil Lennon was also struck with a coin during the Edinburgh derby game.
Hearts manager Craig Levein, meanwhile, has reported “a punch” was aimed at his goalkeeper Zdenek Zlamal by a spectator.
Police confirmed investigations into both incidents were continuing.
Five people were arrested at the match at Tynecastle, which ended in a goalless draw.
It is thought both assistant referees, Frank Connor and David McGeachie, were targeted by individuals in the crowd.
The match commander, Ch Insp Murray Starkey, said: “Police Scotland condemn the mindless acts of violence including missiles being thrown during last night’s Edinburgh derby.
“I can confirm we are investigating two separate incidents involving the Hearts goalkeeper and the Hibernian manager during the match.
“A 25-year-old-man has been arrested and charged for an assault involving the assistant referee.
“A total of five arrests have been made during the evening. Anyone who witnessed these mindless acts should contact the police on 101.”
Hibs boss Lennon was struck “on the jaw” moments after appearing to celebrate Hearts having an injury-time goal disallowed.
After the match, he said: “People will say I was winding the crowd up; I wasn’t. I was just giving a bit back for the abuse I was taking for 90 minutes.”
Hearts owner Ann Budge called on football fans to report incidents of crowd trouble at games.
She told BBC Scotland: “I’m asking our supporters to speak up if they see something of this nature happening.
“We don’t want people who do this sort of thing involved in football. It brings the whole game into disrepute.
“A lot of us are working very hard to try and improve the situation at football and make it an experience that families can enjoy.”