David Gowans, 32, of Aberdeen, has also been banned from attending football matches for 10 years.
The seat hit Aberdeen player Jack MacKenzie above the left eye leaving a two-inch wound which required stitches.
The incident happened on May 17 last year following the final game of the season between Aberdeen and Dundee United at Tannadice.
Gowans was sentenced at Dundee Sheriff Court after he admitted a charge of culpable and reckless conduct.
Helen Nisbet, Procurator Fiscal for Tayside, Central and Fife, said:
“This was disgraceful conduct which could have resulted in far greater consequences.
“David Gowans’ crass behaviour could also have jeopardised the safety of other supporters.
“As prosecutors, we will not hesitate to deal with this type of offending which puts people at serious risk of harm.”
At the time the seat was thrown, a number of Dundee United fans were on the pitch celebrating their team’s victory, which guaranteed qualification for European competition.
A witness saw Gowans, who identified as an Aberdeen Ultra, throw the seat from an upper tier.
Mr MacKenzie, who now plays for Plymouth Argyle, was among a group of Aberdeen players who went over to the nearside stand to applaud their own supporters.
Stadium CCTV footage showed the player falling to the ground and holding his head.
Hours later, Gowans contacted Aberdeen’s Supporters Liaison and Disability officer through WhatsApp but initially denied throwing the seat.
He wrote: “I can’t admit to something that would be extremely bad for me. There’s no evidence of it.”
However, he later confessed and his details were passed to the police who arrested him two days later.
During a police interview, the accused admitted drinking a half litre of vodka prior to leaving home for the match.