The game started at slow pace but Sergio Aguero broke the deadlock in the 19th minute as the game bust to life.
Alfred Finnbogason responded for Iceland in the 23rd minute with their first goal at the World Cup and they hold to a 1-1 draw at halftime.
Lionel Messi had a chance to put Argentina ahead in 63rd minute but lost the penalty.
Messi slated on Twitter for penalty miss
Cristiano Ronaldo and all eyes were on Messi to produce a better performance against Iceland.
Messi's penalty missed a penalty which eventually proved costly and denied Argentina all three points.
Twitter users reacted to the outcome of the result differently as some criticised Messi for an under par performance while some blamed the quality of the team.
Reactions to Messi's penalty miss against Iceland
A fan said, "Messi spent most of the time doing things Dybala will do. I think Sampaoli has to seriously consider playing Dybala as the "real" playmaker & let Messi be free to cause real damage further forward. Just a thought."
Some users were of the opinion that Messi should not be compared to Ronaldo after another penalty miss.
A fan said, "Messi: Anyone can score a penalty. Ronaldo: Take, come and score."
Another said, "Messi fans blaming the defenders, midfielders, wind, pitch, fans inside the stadium, commentators, Sampaoli's bald head but not their goat for missing the penalty which could've won Argentina the game. I love this game!."
Another fan mocked Messi's penalty losing streak for his country, he said, "Messi on International Stage: 2014 Miss Penalty vs Germany. 2016 Miss Penalty vs Chile. 2018 mISS Penalty vs Iceland, Consistency is Key."
A supporter of Messi, said, "EURO 2016 - Iceland shuts down Cristiano Ronaldo and Portugal. Final score: 1-1, Portugal win EURO 2016, World Cup 2018. Iceland shuts down Lionel Messi and Argentina. Final score: 1-1."
Messi and his Argentine teammates will hope to bounce back when they take on Croatia in their next fixture, while Iceland face the Super Eagles of Nigeria on Friday, June 22.