Brendan Rodgers' men secured a straightforward victory in the first leg of the Champions League second-round qualifier in a game marred by spectators throwing missiles at Celtic players.
Griffiths was booked following one such incident, having complained to referee Alejandro Hernandez about a bottle being thrown in his direction as he prepared to take a corner.
After the final whistle, the Scotland international tied a Celtic scarf to one of the goalposts.
— talkingbaws (@talkingbaws) July 14, 2017
UEFA has confirmed Griffiths will be banned for the first leg of Celtic's next Champions League tie against Rosenborg as they seek to reach the group stage of the competition, while the club will be fined €4,500.
Linfield, meanwhile, have been given a partial stadium closure for their next European fixture and a fine of €10,000 as their punishment for the crowd disorder at the game.
UEFA have also handed out fresh charges to Celtic following their 4-0 second-leg victory against Linfield on Wednesday, in which Sinclair struck a brace.
The charges against Celtic include the displaying of illicit banners at Parkhead, stairways being blocked during the tie and a kit infringement, with the case to be dealt with on July 28.
In response to the paramilitary-style banners, Celtic issued a statement that read: "Any support for a paramilitary or proscribed terrorist organisation has no place at Celtic Park.
"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. Events last night have resulted in charges from UEFA in relation to the paramilitary banners and unsafe behaviour in a section of the Celtic support.
"The club has commenced an inquiry and will take appropriate action."