Hearts goalkeeper Zdenek Zlamal was also floored by an apparent attack from a supporter during the goalless match at Tynecastle Park on Wednesday.
Lennon was struck in the face by a pound coin after Hearts player Clevid Dikamona had a stoppage-time goal ruled out for offside.
The game was held up as he received treatment but he was soon back on his feet.
Police Scotland described the incidents as “mindless acts of violence” and said officers are investigating.
The force also confirmed that a 25-year-old man has been arrested in relation to an alleged assault on an assistant referee during the game.
Lennon said: “I’m very, very angry. I’m fizzing about it.
“It’s disgraceful. I don’t blame the club - you can’t legislate for the hatred of some individuals or the badness.
“What possesses people to throw things on to a football pitch I will never know.
“I believe Zlamal was hit as well. It’s just ridiculous. We don’t defend that behaviour from our supporters as well. Hopefully both individuals will be singled out.
“I would like to meet the individual who threw the coin at me some day, because I am not happy about it at all.”
The Irishman was previously assaulted by a Hearts fan on the touchline while Celtic manager.
Zlamal appeared to be struck by the arm of a fan in the Hibs end as he went to retrieve the ball from behind his goal and missiles appeared to rain down as he got up and gestured in defiance.
Chief Inspector Murray Starkey, match commander, said: “Police Scotland condemn the mindless acts of violence which included 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 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.”
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