The Celtic manager was attacked by a man emerging from the stands during his side's 3-0 win. Scottish football authorities have launched an investigation.
A 26-year-old John Wilson, from Edinburgh, has been charged with breach of the peace and assault aggravated by religious prejudice.
Officers arrested him on Wednesday after a fan clambered from the Hearts section of the main stand on to the pitch and lunged at the Celtic boss who was on the touchline at Tynecastle stadium in Edinburgh.
The man was quickly grappled to the ground by Lennon's assistant, former Hoops player Alan Thompson, and immediately arrested by Lothian and Borders Police.
After the game, trouble flared in the Celtic section of the stadium with fans appearing to fight with police and stewards.
Celtic 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 OK.
"I saw someone coming and we didn't react at first, we were obviously shocked and the guy could have had anything in his hands.
"I haven't really had time to speak to Neil, he has a strong character but how much can a guy take?"
A police spokesman said: "A number of incidents took place during this match including some violent disorder.
He has a strong character but how much can a guy take? - Johan Mjallby
"Lothian and Borders Police will fully investigate all of the incidents that occurred at the match this evening and will work closely with both football clubs and the SPL."
Scottish Football Association chief executive Stewart Regan, SPL chief executive Neil Doncaster and Scotland's First Minister Alex Salmond all condemned the incident.
'Arrests made' over parcel bombs
Northern Irish Catholic Lennon has had death threats in the past and in recent weeks was sent two parcel bombs, as were other high-profile Celtic supporters.
In a separate police operation launched on Thursday morning in Kilwinning, Ayrshire, two arrests were made in connection with the investigation into the parcel bombs.
Two parcel bombs were sent to Lennon and one each to lawyer Paul McBride QC and former MSP Trish Godman.
Last month Strathclyde Police said the two packages sent to Lennon, and the two others were "designed to cause real harm to the person who opened them".
A fifth suspect package, addressed to the offices of Cairde Na H'Eireann (Friends of Ireland) in Glasgow, was also intercepted by officers last month.
The match, not only had the usual off the pitch tensions between the two sides, but spilled on to the turf as well in a fiery game that resulted in three sendings off and multiple fracas on the sidelines between players and members of the management teams.
There were 34 arrests inside the stadium and many more outside meant that it was a busy evening for the Strathclyde police force.
This flare-up of the historic rivalry came only a fortnight after the last game between the two sides, which resulted in 229 supporters being detained and all the city's police cells being filled.
A brief history of one of sports most violent and political rivalries
The history of the rivalry between the two clubs has its basis in sectarian animosity, either on a Catholic (Celtic) versus Protestant (Rangers) divide or tied around the politics of Northern Ireland, pitting Loyalist against Republican sympathies. As a consequence the rivalry did not gather its modern spice until after 1912 as the problems in Ireland escalated. Rarely will a St Andrews flag be seen at Ibrox or Celtic Park as over the years they have been replaced with the more politically-symbolic Union Jack and Irish tricolore.
Since the Second World War only three players have appeared for both clubs, the most recent being Kenny Miller, Scotland's current captain. A 1980 fixture between the two sides saw the worst-ever reported pitch invasion at a football match, as fans had an on-pitch battle at the National Stadium Hampden Park, following Celtic's 1-0 win in the Scottish Cup Final. This led directly to the banning of alcohol in Scottish grounds on match days.
One of the four fixtures between the clubs in 1998 saw perhaps the most inflammatory gesture from a player towards opposition fans ever. England's Paul Gascoigne mimicked playing the flute, a Loyalist image, to the Catholic Celtic faithful, causing outrage amongst fans in the ground and those watching the game live at home. The player was fined £20,000.
In 1999 missiles were thrown on to the pitch during a derby at Celtic Park, striking the referee Hugh Dallas and leading to the game to be stopped whilst he received treatment. At least four fans came on the pitch that day to directly confront the referee. This led to Old Firm games being arranged as early evening kick-offs, where possible, and an avoidance of Firm games being title deciders.
2011 and the cells were full up in Glasgow after February's clash between the two teams, with some arrested individuals being taken as far away as 50 miles to be detained. Two weeks later and battles on the pitch led by Senegalese player El Hadji Diouf, a player who has had numerous disciplinary problems in the past, spark yet more sectarian and racial violence in the stands and out on the streets of Glasgow.