According to rule 2.6 of the competition, participating broadcasters are required to ensure their performers take “all necessary steps” to ensure the Song Contest is not politicised or instrumentalised.
Hatari’s members are known supporters of the Israel boycott movement BDS.
The ESC did not reveal how much it had fined RÚV but said it was “in line with the rules of the competition” and that the penalty was upheld following an appeal.
The Netherlands went on to win the contest, which came to Tel Aviv after Netta Barzilai won for Israel last year.
The grand final also saw a performance by Madonna, who provoked controversy when two of her dancers appeared on stage with Israeli and Palestinian flags on their costumes.
A spokesperson for the EBU said: “During the Grand Final of the Eurovision Song Contest 2019, the Icelandic artists Hatari displayed a banner on screen breaching rule 2.6 which prohibits the politicization of the event.
“In response to this, and to ensure the values of the Eurovision Song Contest are respected, the Eurovision Song Contest Reference Group decided that Icelandic EBU Member RÚV should receive a punitive fine, in line with the rules of the competition.
“Following an appeal by RÚV, the decision was upheld by the EBU Television Committee.”