The Scottish team drew 0-0 with Maribor in the match at the Ljudski Stadion on Thursday evening.
Slovenian Police said five Scottish citizens and one Austrian were arrested after clashing with police officers in Mladinska Ulica street as they were being escorted towards the stadium.
None of the police officers were injured and the Scots were released by 6am on Friday.
Police said criminal complaints will be filed against them at the Prosecutor’s Office.
A Maribor Police spokesman said: “During the escort, at the Mladinska Ulica street, six foreign (five Scottish and one Austrian citizen) citizens suddenly started to attack police officers with punches and different objects.
“The police officers subdued, arrested and detained them. Criminal complaint will be filed at the competent Prosecutor’s Office against five (four Scottish citizens, one Austrian citizen) of them and a fine was imposed on the person (Scottish citizen), whose punch was blocked by the police officer.
“None of the police officers were injured during the attack. The investigative judge on duty and public prosecutor on duty were informed of the criminal offence.
“After the conducted hearings, all foreigners were released by the 6.00 in the morning.”
Police said two Scottish citizens were fined shortly after 5pm for provoking fights with home supporters, while a third was fined as officers began escorting foreign supporters from the Grajski trg square towards the stadium.
Another Scot was fined for provoking a fight and ignoring police orders and was later taken to the University Medical Centre (UKC) Maribor due to health problems and “severe intoxication”, police said.
A fifth Scottish citizen was also fined for disruptive behaviour.
Meanwhile a Scottish woman was taken to the University Medical Centre after she was exposed to tear gas during the police intervention.
She was released from the hospital after treatment.