They met in the final Group H match at the 1998 World Cup in France, and with qualification assured, a 36th-minute victor by defender Mauricio Pineda was enough for the South Americans to top the group.
Except for France 1998, Nigeria have faced the two-time world champions in all their world cup campaigns.
Messi and Argentina have lost three straight finals at major competitions in a three-year span, with the first coming at the 2014 World Cup against Germany.
Argentina did not book their spot in Russian Federation until their final qualifier, a 3-1 win at Ecuador on October 10, with captain Lionel Messi scoring a hat trick.
Super Eagles technical adviser Gernot Rohr has suggested that the June 27th clash between Nigeria and Argentina could determine his team's progress at the 2018 world cup in Russian Federation.
Five-time World Player of the Year Messi, 31, will once again be required to provide inspiration at possibly his last World Cup, but with a plethora of attacking talents such as Sergio Aguero, Angel Di Maria and Paulo Dybala, Jorge Sampaoli's men will be favourites to score the goals required to progress.
The most tantalising group-stage clash will be Group B's first game between European champions Portugal and 2010 winners Spain on June 15 in Sochi.
"We know about Argentina, they are a good team".
The first and only time Nigeria met Iceland was in an worldwide friendly in Reykjavik, August 22, 1981, Nigeria lost 3-0.
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After the Albiceleste were placed in Group D with Croatia, Iceland and Nigeria.
We have a young team and we are going to the World Cup to go and learn.
The Yugoslavs, who then included the Croats, won 3-0.
Croatia, who finished second, qualified via the playoffs after six wins, two draws and two losses.
"World Cup baby", Balogun wrote.
They finished third on their debut in 1998, but have since failed to go past the group stage in 2002, 2006 and 2014.
"Argentina have one of the strongest squads in football. the Nigerian players are great athletes, physically strong and it's hard to cope with them".
Iceland won its qualifying group in October ahead of Croatia which was runner-up.