Brown was involved in three separate incidents during Celtic’s 2-1 win over Rangers at Celtic Park.
The win all-but secured The Bhoys will win their eighth straight Scottish Premiership title.
Celtic are now 13 points clear of their arch rivals at the top of the table.
Sunday’s win was made even more sweet for home fans as they saw two Blues players sent off for off-the-ball incidents.
After just half-an-hour, controversial striker Alfredo Morelos was sent off for elbowing Brown in the face as the pair ran back over the halfway line.
Then, after the final whistle blew, Brown ran over to celebrate in front of the travelling Rangers fans, in a move which incensed Andy Halliday.
The Rangers midfielder ran over to Brown and shoved him, causing a mass brawl.
Halliday was sent off in the tunnel.
Many fans believed that Ryan Kent should also have been sent off for punching the Celtic captain in the face soon after the winning goal was scored, but referee Bobby Madden did not see the incident.
And Hartson criticised the Rangers player involved, saying in his Glasgow Evening Times column that Brown hadn’t done anything wrong.
“Alfredo Morelos, it has been claimed, was provoked. Okay, maybe he was,” he wrote.
“But then it’s up to him what happens next.
“There is no excuse, no reason on earth, why he had to smash Scott Brown in the face with his elbow.
Also, Andy Halliday ran half the length of the pitch to get involved after the final whistle.
“Did he feel provoked? If so, it’s them up to him how he reacts.
“And then there is Ryan Kent who will be done for his behaviour. Was his excuse also that he felt provoked? My goodness.
“There is no justifiable reason for him punching Brown, full blown, in the face.
“Provoking an opponent is part of the game. It happens all the time.
“It began over 100 years ago. It will always be part of football.