In a statement, Scottish Football Association chief executive Stewart Regan condemned the attack.
Lennon was attacked by the fan after Gary Hooper had put the visitors two goals ahead in a game Celtic went on to win 3-0.
Before the game could restart a fan clambered from the Hearts section of the main stand and made a beeline for the Celtic boss who was on the touchline, leading to an intervention by police and stewards after the fracas ended and the supporter was taken away by police. Trouble ensued in the Celtic section of the stadium with fans appearing to fight with police and stewards.
Regan said: “Clearly this kind of behaviour from supporters is wholly unacceptable.
“The safety of players, club officials and match officials is paramount on or around the field of play, and this clear breach of security is a matter I will be discussing with SPL chief executive Neil Doncaster tomorrow.”
Lennon’s assistant manager Johan Mjallby said: “What has happened to Neil is a dark day for Scottish football and I’ve never seen anything like it, he is shaken but okay,” he said.
“I saw someone coming and we didn’t react at first, we were obviously shocked the guy could have had anything in his hands.”
Lennon has been in the headlines regularly this season for incidents on and off the field. He received a touchline ban in November while in January a package addressed to him containing bullets was intercepted at a sorting office in Co Antrim.
On April 19 it emerged that Royal Mail intercepted a total of two “viable” parcel bombs addressed to Lennon.