Hibs boss Neil Lennon appeared to be struck by a coin during the Scottish Premier League game at Tynecastle, while Hearts manager Craig Levein said his goalkeeper Zdenek Zlamal was hit by a supporter.
Both assistant referees also appeared to be struck by missiles and a police statement confirmed a man has been charged, with five arrests made in total.
"Police Scotland condemn the mindless acts of violence which included missiles being thrown during last night's Edinburgh derby," said chief inspector Murray Starkey, match commander, in a statement released to Omnisport.
"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 in relation to an assault involving the assistant referee. A total of five arrests have been made. Anyone who witnessed these mindless acts should contact the police on 101."
Levein and Lennon both condemned the violence that marred a top of the table clash between the Edinburgh rivals.
"They will get dealt with. I just think it's abhorrent," said Levein after the match. "I don't mind people being committed fans who are aggressive in their support, but throwing things isn't on.
"The stadium itself is fantastic with fans right on top of the players. At times it can be a bit like a cauldron. I'm just disappointed it happened and I got a fright when I saw Lenny [Lennon] lying on the ground. There's no place for that.
"Bobby [Zlamal] says someone struck him and it looks like Neil has been hit by a coin. It just saddens me, really. Both sets of players are doing well at this moment in time, they don’t want to get beat, tension is high, aggression is evident throughout the match on the field. But there's no place for things like that.
"You can sing and shout and swear all you like, but not that. I got a fright when I saw Lenny on the ground. I hope they catch whoever it was who threw it, it doesn't matter what team they support, they need to be dealt with."
Lennon was felled after turning to the home fans to celebrate a late goal for Hearts being disallowed.
"It's unsavoury to say the least. It's unacceptable," Lennon 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."
The game ended 0-0, leaving Hearts four points clear at the top of the Scottish Premiership table.
Last month, police charged a man accused of assaulting an assistant referee during the Scottish Premiership match between Livingston and Rangers.