Meanwhile, Bayern Munich forward Thomas Mueller and Ajax Amsterdam defender Maximilian Woeber will miss both legs of their teams' respective Champions League round of 16 ties after being banned for two European games following red cards last month.
Mueller will sit out the tie against Liverpool and Woeber misses his side's clash with Real Madrid.
Lovren posted a video on Instagram where he appeared to brag about elbowing Real Madrid defender Sergio Ramos and made insulting comments about the Spain team following the game on March 15.
He also told reporters after the match that Spain were "rude on the pitch" and bad losers.
UEFA said that Lovren had fallen foul of a clause in its disciplinary rules which penalises anyone "whose conduct is insulting or otherwise violates the basic rule s of decent conduct."
He was suspended from Croatia's next UEFA competition match, which is the Euro 2020 qualifiers at home to Azerbaijan in March.
Despite the win, Croatia finished bottom of Group A4 after losing their final game to England and were relegated to League B of UEFA's new competition.
Mueller was given a straight red card for a high kick on Nicolas Tagliafico during Bayern's 3-3 draw against Ajax and was banned for two European club matches. Woeber was dismissed in a separate incident of the same match.
BATE Borisov's Sihnevich Mikalai and Villarreal's Costas Jorda Jaume were also banned for two European matches after being sent off in Europa League games last month.
Olympiakos were fined 90,000 euros (£80,920) following crowd trouble in their Europa League match against AC Milan.
UEFA sanctioned the Greek side over a pitch invasion, the setting-off of fireworks and blocked stairways during their 3-1 win over Milan on Dec. 13 in Athens.
Olympiakos must play their next home match behind closed doors although this was deferred for a "probationary period" of two years.
Milan coach Gennaro Gattuso suggested that Olympiakos threw extra balls onto the pitch and mentioned a "strange trumpet noise" although he said it was not an excuse for their defeat.
Milan were fined 5,000 euros after their fans also set off fireworks.
Paris St Germain and Red Star Belgrade were fined 35,000 euros and 25,000 euros respectively for incidents at their Champions League match on Oct. 3 which the Ligue 1 side won 6-1.
(Writing by Brian Homewood; Editing by Christian Radnedge)
