The Irish League champions have also been ordered to partially close the South Stand Lower section of the stadium at Windsor Park for any next UEFA fixture as the host club.
Penalties have been imposed against the Blues over missiles thrown by fans and a pitch invasion at their Champions League qualifying first leg game last Friday.
Linfield have promised a full investigation and to hunt down those involved and robustly deal with them.
Celtic’s Leigh Griffiths has also been banned for one UEFA game for “provoking spectators” by tying a Celtic scarf around a goalpost after the final whistle.
The Glasgow side were fined €4,500 for improper conduct after the team picked up five yellow cards during the Champions League qualifiying match.
The Hoops are also facing more sanctions after Wednesday’s second leg encounter at Celtic Park.
They have been charged over a paramilitary-style banner, for blocked stairways and a kit infringement.
In a statement, Celtic condemned the behaviour leading to the charges.
“Any support for a paramilitary or proscribed terrorist organisation has no place at Celtic Park,” the club said.
“The club has been consistent in condemning such conduct on the very few occasions in the past when it has occurred at Celtic Park.
“It is unfortunate that such a small minority of the crowd at Celtic Park last night behaved in such a way. We know that the Celtic support will join us in condemning such behaviour.”
Celitc will know what its punishment will be next Friday, July 28 followiong a meeting of the UEFA’s Control, Ethics and Disciplinary Body.