Aberdeen defender Jack MacKenzie suffered a head injury after being hit by a seat thrown by his club's supporters in the aftermath of a 2-1 defeat to Dundee United on Saturday.
United leapfrogged Aberdeen into fourth place on the final day of the season after coming from behind at Tannadice.
A section of home fans invaded the pitch at full-time and some goaded the Aberdeen travelling support.
The seat was thrown in retaliation but struck MacKenzie, who had been an unused substitute in the match.
"This is unacceptable and can't happen," said Aberdeen manager Jimmy Thelin.
"We have to get all the facts of what actually happened. All we know is Jack got a really bad injury as a player doing his job. This cannot happen in this way."
A restricted number of Aberdeen fans were in attendance after objects were aimed at United manager Jim Goodwin in the last meeting between the clubs at Tannadice.
James Forrest spared Celtic's blushes on the day they lifted the Scottish Premiership trophy with a stoppage-time equaliser in a 1-1 draw against St. Mirren.
Forrest recently became the Glasgow giants' most decorated player of all time with a 26th major honour.
The 33-year-old's strike ensured he scored for a 16th consecutive season as Celtic avoided just a second home domestic defeat of the season.
Jonah Ayunga's deflected opener early in the second half had boosted St Mirren's dream of European football.
But they had to settle for sixth place as Forrest drilled in at the near post in the 94th minute.
"It was an amazing finish to the game. It is a testament to his tremendous professionalism and hunger. He is so disciplined in his profession," said Celtic manager Brendan Rodgers.
"He clearly has an emotional attachment to the club – he has been here since he was young and to have lasted this long at a club like this, you have to be doing so many things right and you also need to be performing."
Celtic ended the campaign 17 points clear of Rangers as the runners-up were also held 2-2 at third-placed Hibs.
After Cyriel Dessers' second-minute opener put the visitors in front at Easter Road, Rangers thought they had doubled their lead through Nicolas Raskin.
However, VAR could not find a definitive angle to prove the ball had crossed the line, and Hibs controversially raced up the field to level through Kieran Bowie.
Raskin's header restored Rangers' advantage in the second half.
Hibs, though, capped their fine season as Martin Boyle secured a point. (AFP)