• SFA chief executive Stewart Regan called the incident a 'blight on the image of Scottish football'
Stewart Regan issued a statement on behalf of the governing body echoing the widespread condemnation of the incident.
Lennon, who has been a target for sectarian hatred throughout his career as a player and manager, came under attack from a man who had climbed over the barrier and ran along the touchline, before being tackled and led away by police.
A 26-year-old man is due to appear at Edinburgh Sherrif Court today.
Although the SFA do not have a direct remit over the incident, Regan welcomed the Scottish Premier League's investigation and called on clubs to ensure the safety of players and officials.
In the statement, he said: "In discussions with Neil Doncaster this morning, the Scottish Premier League (SPL) have confirmed they have initiated an investigation into the unsavoury events at Tynecastle last night.
"I am also aware that Heart of Midlothian are carrying out their own review of internal security measures at the club and have agreed to cooperate fully with both the police and the football authorities.
"I reiterate my condemnation of this blight on the image of Scottish football and expect to see robust plans in place to protect players and officials at all times."
Hearts will face serious questions from the SPL over how the man was able to breach security and reach Lennon in his technical area.
The security around the Tynecastle technical area appeared to be light, and on a night of heightened tensions within the stadium, there has been criticism of the stewards and police for failing to stop the pitchside intruder getting near Lennon.
Any possible sanctions could be influenced by the fact that it is not the first such incident at the stadium. Two Hearts fans were banned indefinitely after confronting Hibernian striker Derek Riordan after he had scored in a 2009 derby match.
SPL chief executive Neil Doncaster told Sky Sports News: "We'll be focusing on the situation that led to him being able to get access to the perimeter track and that's something we'll be discussing in detail with the home club.
"The investigation started immediately the incident happened last night. We'll be talking with the SFA and with all the parties involved to investigate it as thoroughly and as speedily as possible."
Doncaster added: "We'll be certainly talking to both clubs, the police and also to our own match delegate, who witnessed the incident, and taking reports from all of those and investigate it thoroughly.
"It's absolutely vital that any lessons that need to be learned are learned and we can put them into effect."
Hearts also confirmed they are investigating the security breach.
A statement on the Hearts FC website stated their plans: "Heart of Midlothian FC can confirm that a full investigation into the events which took place in the second half of tonight's game against Celtic is underway.
"Hearts is a club which prides itself on its "football for all" policy and these sorts of actions have no place in the game of football.
"We will give our full support to the stewards and the police authorities in the ensuing investigation into the events at tonight's match."
Last night Lennon used his Twitter page to praise his team's performance in the 3-0 win that keeps their title hopes alive.
He wrote: "Don't let what happened to me tonight take the shine off a wonderful team performance... I don't walk alone."
Speaking on behalf of Celtic, Lennon's assistant Johan Mjallby said he was "shocked" by the events he witnessed.
On the Celtic FC website, Mjallby said the attack was a "disgrace".
"Neil was shocked, and obviously, he's had death threats and he's shaken right now," Mjallby said. "I have never seen anything like it."
The Swede continued: "We have to look into this because when you work in management you should be secure in a football ground.
"I was shocked like everyone else in the dugout. We were focusing on the game and trying to get the three points to take it to the final game. Usually I can talk about football and I prefer to do that.
"Neil's a strong character and he's coped with a lot this season and has still been able to work with this team and improve it, so we'll have to wait and see how he feels, but we're all desperate for him to continue doing his work."
When asked for his thoughts, Hearts boss Jim Jefferies said there was a "hostile" atmosphere in the ground for the match.
"It was unbelievable," Jefferies said. "For someone to try and deliberately attack another person on the touchline is nothing short of disgraceful."
"There was a bit of hostility in the air and the atmosphere tonight, but I don't think anyone thought that it would result in what happened."
Jefferies also said that he hoped the club would avoid any sanctions as a result of the incident.
"I'm sure the club will work fully with the police and the relevant authorities and we'll make sure this sort of shocking thing never happens again," he said.
"It should never get to this. We were looking forward to a good celebratory atmosphere tonight and unfortunately it never turned out that way."
He also confirmed he had spoken to Lennon to offer him his support: "Neil and Johan (Mjallby) thanked us for the gesture, and although he seemed shocked and shaken, I'm sure he'll be fine".