David Gowans, 32, hurled the object onto the pitch following Aberdeen's 2-1 loss away to Dundee United at Tannadice on May 17 last year.
It struck Aberdeen defender Jack MacKenzie, who was thanking travelling Dons fans for their support in the Scottish Premiership fixture.
MacKenzie suffered a deep laceration to his left eyebrow and an abrasion below his eye.
Gowans, who had been a member of the Aberdeen ultras supporters' group, admitted culpable and reckless conduct in October.
Passing sentence at Dundee Sheriff Court, judge Alastair Carmichael told Gowans: "Your actions were selfish, stupid, dangerous and utterly irresponsible. You must have known that by throwing this item it could hit somebody".
Gowans was sentenced to 18 months in prison and handed a banning order, barring him from attending football matches for 10 years.
He had already received a lifetime ban from Aberdeen Football Club.
His lawyer, Larry Flynn, told the court his client had been drunk at the time he threw the seat and was "extremely embarrassed" over the incident.