Both teams were also fined over incidents at their second qualifying round first leg tie last Friday, which Celtic won 2-0.
UEFA said it had opened further disciplinary proceedings against Celtic following their 4-0 win in Wednesday's return leg in Glasgow.
Friday's first leg was marred when fans of Irish Premiership champions Linfield threw objects on to the pitch and invaded the playing area at the end of the game.
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UEFA said Linfield would be ordered to close the lower section of the south stand at Windsor Park at their next home European tie. They were also fined 10,000 euros ($11,630).
Griffiths, who had a bottle thrown at him, was given a one-match suspension and will miss the game at home to Norwegian champions Rosenborg on July 26. His team were fined 4,500 euros for misconduct after receiving five yellow cards.
The match had been identified as politically charged.
Media reports said Griffiths tied a Celtic scarf around the Windsor Park goalpost and made a 5-1 gesture - a reference to the predominantly Catholic side's win over Glasgow rivals Rangers, a Protestant club with close ties to Linfield.
Police in full riot gear, backed up with dogs, ended the Belfast game on the pitch keeping rival fans apart after several hundred Celtic fans obtained tickets, despite the Scottish club's decision not to take up their allocation.
UEFA said the new proceedings against Celtic were over an "illicit banner" displayed by fans, blocked stairways in the stadium and a "kit infringement" in Wednesday's second leg.
Meanwhile, Macedonian champions Vardar Skopje have been charged with throwing of objects by fans, crowd disturbances, blocked stairways, illicit chants and setting off of fireworks during Tuesday's 3-1 win over Malmo.
(Writing by Brian Homewood in Berne; Editing by Christian Radnedge)
