Messi broke free on the left side and tried to go for the far post but the ball rolled wide of the Germany goalkeeper Manuel Neuer and his net. Messi again shot wide in the 75th.
Germany had a chance in the 71st, with the ball bouncing between players in front of goal, but Andre Schuerrle couldn't get control.
Argentina had the better chances in the first half, and forward Gonzalo Higuain was the most dangerous player.
The Napoli striker missed a great chance to put his team ahead in the 21st minute, shooting wide after an errant headed backpass. He then had a goal ruled out for offside in the 30th.
Germany was forced to play without Sami Khedira, who pulled out of the starting lineup minutes before kickoff and was replaced by Christoph Kramer.
Kramer, however, was first injured in the 18th minute and then was replaced by Schuerrle in the 32nd with what appeared to be head injury.
Schuerrle, who scored the last two goals against Brazil in the 7-1 semifinal rout as a substitute, then had Germany's best chance in the 37th, but Argentina goalkeeper Sergio Romero made the block.
Benedikt Hoewedes had an injury-time header hit the post.
The match at the Maracana Stadium kicked off with Germany wearing its traditional white shirts and Argentina playing in dark blue.
With Messi in the starting lineup, Argentina has one of the best players in history on the field. The four-time world player of the year has had a stellar World Cup so far, and a win on Sunday will give him the one major title he is missing.
For Germany, a team led by Philipp Lahm and Bastian Schweinsteiger is trying to finally win a major trophy after a nearly 20-year wait.
The Germans, whose last major title came at the 1996 European Championship, reached the World Cup final in 2002 and the semifinals in 2006. They also reached the final at Euro 2008 and the semifinals at Euro 2012.
Historically, however, Germany has been a consistent winner. The national team is trying to win its fourth World Cup, but the first for a united country. West Germany won in 1954, 1974 and 1990, while a united Germany lost in the 2002 final to Brazil.
Argentina is a two-time champion, winning titles in 1978 and 1986.
The last World Cup title for each team came against the other. The Argentines, led by Diego Maradona, beat West Germany in Mexico in the 1986 final, while the Germans leveled the series by winning four years later in Italy.