There have now been a total of 102 arrests since the match between Hibernian and Rangers at Hampden Park. Fans spilled onto the pitch after the final, which Hibernian won 3-2.
The latest men arrested are aged 17, 18, 22, 32 and two men aged 23.
Police Scotland confirmed a report would be submitted to the procurator fiscal.
A dedicated email address has been set up for anyone with information.
They can also contact Greater Glasgow CID on 0141 532 5457 or provide information anonymously via Crimestoppers.

So-called mathematics anxiety was found especially in countries which were more developed and where males and females were considered more or less equal.
University of Glasgow researchers looked at achievements, attitudes and emotions around maths and found girls showed more negative emotion about it.
Data was collected from 500,000 15-year-olds in 68 countries.
Mathematics anxiety is defined as "negative feelings experienced during the preparation of and engagement in maths activities".
Academics, led by Dr Gijsbert Stoet, from Glasgow University's school of education, said it did not seem to matter whether the girls' mothers worked in related fields and that efforts to attract more women into science, technology, engineering and mathematics subjects had largely failed.
Dr Liberty Vittert, a lecturer at the School of Maths and Statistics at University of Glasgow, told BBC Radio Scotland's Good Morning Scotland programme that mathematics anxiety could hamper future job prospects.
Dr Vittert said: "When I was about 14, I had a maths teacher who called my parents into school to say that I couldn't do maths and I should stop and there was no point in further continuing with it.
"It really stops you with jobs if you stop with maths young.
"So I pushed through and I had an undergrad in pure mathematics from MIT (Massachusetts Institute of Technology) and now I have my Phd. So I think it's very important, but I think there's a lot of pressure on young girls to not do some subjects."
Asked if maths had caused her anxiety at school, she said: "Absolutely. I think when you have teachers or other authority figures telling you that you can't do something, of course it creates huge anxiety.
"And clearly there are pressures on a young girl not to do these things."
She added: "If you think about maths, there is always a right or a wrong answer. Whereas in some subjects such as English, there aren't always right or wrong answers.
"So if you can't get that exact answer, the teacher can just say, 'Well you don't know what you're doing, you're not smart.'
"Whereas maybe you just don't quite get it.  In English you can have varying levels of understanding."

Police Scotland said the emergency services were alerted to the incident at about 13:00.
A coastguard helicopter and lifeboat joined rescue teams looking for the man.
A post on the RNLI Montrose Lifeboat Facebook page said it had been stood down at 18:20 "due to failing light".
A further six men have been arrested in connection with violence and disorder at the Scottish Cup Final in May.
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Girls are "more afraid" of mathematics than boys in 80% of countries, according to a new study.
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