The incident happened after Forest edged out the Blades to move into the final and one win from a return to the Premier League.
Forest season ticket holder Robert Biggs - from Ilkeston, Derbyshire - admitted assault occasioning actual bodily harm. Sharp was left requiring four stitches to a wound to his lip.
He was jailed at Nottingham Magistrates' Court on Thursday for 24 weeks.
Prosecutor Marianne Connally said the incident was caught by cameras covering the Championship semi-final for live television.
She told the court: "A large number of fans entered the field of play.
"Mr Sharp hadn't directly participated in the game. He appears to be standing with his hands in his pockets.
"Mr Biggs can be seen to run along the pitch. He then headbutts Mr Sharp.
"The Crown's case is that this is a deliberate and senseless act of violence."
Biggs appeared in court in custody and did not oppose an application for a football banning order during the hearing.
He was told that a separate charge of illegally entering the playing surface had been dropped.
District Judge Grace Leong said while sentencing: "The video clip proves to me that you were running towards Billy Sharp and that you dodged all the other spectators to get towards him.
"I am of the view that it was a targeted act of aggression... even if it was not premeditated.
"You must have seen him fall over but you did not stop to check if he was all right or whether he was seriously injured."
The judge was asked to give Biggs a suspended sentence after it was claimed he and his girlfriend would be unable to keep up with monthly mortgage repayments if he went to jail.
However, the judge said: "Given the gravity of this offence, where thousands were present to witness it, there has to be an element of deterrence."
The judge added the attack could have "given rise to further incidents".