Celtic have been fined £7,500 and handed a suspended reduction in capacity for fan behaviour.
The SPFL announced the penalties for pitch invasions and pyrotechnics during the last games of the previous season.
The most notable event was at Parkhead, when Celtic fans stormed the pitch following a goal against Hearts.
This led to concerns over player safety as Hearts players exited the stadium promptly.
Celtic's match against Motherwell also involved pitch invasions and pyrotechnics.
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The SPFL has imposed a suspended reduction of 100 tickets for one away game on Celtic.
This will be activated by future incidents involving away fans.
For the final day disturbances, a further suspended reduction of 1,000 seats for one home game has been imposed.
Motherwell face similar action, with a suspended closure of Block E in the East Stand, also dependent on future fan behaviour.
An SPFL spokesperson said: "Supporters entering the field of play in any circumstances is wholly unacceptable and puts players, fans and match officials at significant risk of physical harm.
"The use of pyrotechnics at matches is illegal and highly dangerous."
He added: "The SPFL has been repeatedly clear that there is no place for this behaviour in Scottish football. We will continue to work together with stakeholders, including the Scottish FA, Police Scotland and Scottish Government, to address challenges surrounding unacceptable conduct at matches."
In League One, Hamilton Accies, Inverness, and Stenhousemuir have all been handed suspended punishments for incidents.
