Meanwhile, Bayern Munich forward Thomas Müller 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.
Müller will sit out the tie against Liverpool and Woeber misses his side's clash with Real Madrid.
Liverpool's 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.
