They are alleged to have taken insufficient action to stop missile throwing and violent, threatening and racist behaviour at Upton Park.
West Ham are also accused of failing to prevent their fans invading the pitch.
The FA has convened a disciplinary hearing where an independent three-man panel, chaired by a QC, will consider evidence.
A verdict will be announced on Friday at the earliest, with the possibility of a decision being adjourned until next week.
Wide-ranging sanctions are available, although it is thought a heavy fine or suspended sentence would be most likely if either club is found guilty of any charge.
The Hammers face four charges, while Millwall must answer three.
Both clubs face charges of failing to ensure their fans refrained from:
- Violent, threatening, obscene and provocative behaviour
- Racist behaviour
- Throwing missiles, harmful or dangerous objects on to the pitch
West Ham are also charged with failing to ensure their supporters did not enter the field of play.
A Millwall supporter was stabbed as fans clashed outside the east London ground and pitch invasions by West Ham fans followed each of their side's goals in the 3-1 extra-time win.
More than 20 people have been charged in connection with disorder inside and outside the ground.
Nine of those pleaded guilty at Stratford Magistrates' Court in November to charges including pitch invasion, violent disorder and criminal damage.
Sentences ranged from £150 fines to three-year bans from football games. Another 13 people are due to appear in court in January.
West Ham's Carlton Cole and Millwall's Jason Price alleged they were racially abused by supporters at the match.
Millwall chief executive Andy Ambler has said he considers the charges to be unjustified, and brought in barrister Jim Sturman QC to draft their defence.
"We will be pleading not guilty to all charges and defending our position vigorously," said Ambler.
"It is a frustration to us that we are committing significant resources of time, energy and money towards having to defend ourselves in the face of these charges."
When the charges were announced on 28 September, Millwall said they were "shocked and disappointed".
"It was widely acknowledged that none of our supporters came on to the pitch and indeed the behaviour and forbearance of our fans brought praise from media observers on the night," said a club statement.
"Our question for the Football Association is what can Millwall Football Club do to control individuals' actions once inside our opponents' stadium?"
West Ham also maintain they did as much as they could prior to the fixture.
"We do acknowledge the appalling behaviour of a minority of fans inside the stadium and, in conjunction with police, will continue to take strong and appropriate action against anyone found responsible," said a Hammers spokesman.
An FA statement alleged the clubs did not ensure their supporters conducted themselves in an orderly fashion "in and around the ground".
Police say the 44-year-old Millwall supporter who was stabbed did not suffer life-threatening injuries.
Hundreds of supporters were thought to have turned up for the game without tickets.
It was the first time the east London rivals had played each other since April 2005.
Eyewitness reports suggested opposing fans threw bottles and bricks at each other and started small fires as police moved in to try to quell the disturbances outside the ground.
Inside the stadium, police and stewards battled to remove fans from the pitch throughout the match.
Source: BBC Sport
Source: BBC Sport