The game will be played at Emirates Stadium, the home of the Gunners. The last time the two countries met was during a tournament in Brazil in 1972 when Portugal won 3-1.
The AFA said on its website that Argentina would also play friendlies against the United States in Seattle on March 26 and Costa Rica at the inauguration of their new national stadium in San Jose three days later.
Argentina and Portugal have both scored four goals against world champions Spain in friendlies since the World Cup.
They have also both played at Arsenal's Emirates Stadium before, in friendlies against Brazil.
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