Crespo won his first cap for Argentina in a friendly match against Bulgaria in February 1995.
He was a member of the Argentina side that finished runners-up in the 1995 King Fahd Cup, the predecessor to the FIFA Confederations Cup.

In 1996, Crespo was a member of the Argentina men's football squad for the Olympic Games.
Crespo helped take Argentina to the final with braces against Spain in the quarter-final and Portugal in the semi-final.
However, Argentina lost the final to Nigeria, despite Crespo scoring his sixth goal of the tournament from the penalty spot.

Crespo scored his first goal for the Argentina senior team in a 1998 World Cup qualifier against Ecuador and hit a hat-trick against FR Yugoslavia in a pre-World Cup friendly.
Crespo was called up to the final roster for the 1998 World Cup but only made one substitute appearance, as Gabriel Batistuta led the Argentine attack.
Crespo's attempt was saved by David Seaman in the second round penalty shoot-out with England, but Argentina progressed 4–3.

During qualification for the 2002 World Cup, Crespo was top scorer for Argentina with nine goals as they topped the South American group.
During the finals, Batistuta was again preferred to Crespo as Argentina's starting centre forward.
Crespo appeared as a substitute in all three group matches, including the final match against Sweden, which Argentina needed to win in order to qualify for the second round.
Though Crespo scored an 88th-minute equaliser, it was not to be enough and Argentina were eliminated.

After the 2002 World Cup, Batistuta retired from international football, and Crespo took over as Argentina's number 9.
During the 2006 World Cup qualifying stage, Crespo scored seven times, including two goals in Argentina's 3–1 win over arch-rivals Brazil in Buenos Aires, which sealed qualification and made him Argentina's career scoring leader in World Cup qualifiers.

Crespo scored Argentina's first goal of the 2006 World Cup in their opening match against the Ivory Coast.
He also scored in the next game against Serbia and Montenegro (6–0) and the second round match against Mexico.
However, Argentina's run was ended as they were knocked out by host nation Germany on penalties in the quarter-final.

Crespo's final appearances for Argentina came at 2007 Copa América.
He scored twice in Argentina's 4–1 victory over the United States in their Group C opener, tying Diego Maradona's team scoring record.
He then overtook Maradona in Argentina's second match, scoring a penalty kick against Colombia.
However, he substituted immediately after converting the kick due to injury and missed the remainder of the tournament.

After the Copa América, Crespo did not receive any further call-ups to the national team and ended his international career with 35 goals in 64 matches, making him Argentina's third highest goalscorer of all-time, behind Gabriel Batistuta and Lionel Messi.
Crespo won his first cap for Argentina in a friendly match against Bulgaria in February 1995. He was a member of the Argentina side that finished runners-up in the 1995 King Fahd Cup, the predecessor to the FIFA Confederations Cup.
In 1996, Crespo was a member of the Argentina men's football squad for the Olympic Games. Crespo helped take Argentina to the final with braces against Spain in the quarter-final and Portugal in the semi-final. However, Argentina lost the final to Nigeria, despite Crespo scoring his sixth goal of the tournament from the penalty spot.
Crespo scored his first goal for the Argentina senior team in a 1998 World Cup qualifier against Ecuador and hit a hat-trick against FR Yugoslavia in a pre-World Cup friendly. Crespo was called up to the final roster for the 1998 World Cup but only made one substitute appearance, as Gabriel Batistuta led the Argentine attack. Crespo's attempt was saved by David Seaman in the second round penalty shoot-out with England, but Argentina progressed 4–3.
During qualification for the 2002 World Cup, Crespo was top scorer for Argentina with nine goals as they topped the South American group. During the finals, Batistuta was again preferred to Crespo as Argentina's starting centre forward. Crespo appeared as a substitute in all three group matches, including the final match against Sweden, which Argentina needed to win in order to qualify for the second round. Though Crespo scored an 88th-minute equaliser, it was not to be enough and Argentina were eliminated.
After the 2002 World Cup, Batistuta retired from international football, and Crespo took over as Argentina's number 9. During the 2006 World Cup qualifying stage, Crespo scored seven times, including two goals in Argentina's 3–1 win over arch-rivals Brazil in Buenos Aires, which sealed qualification and made him Argentina's career scoring leader in World Cup qualifiers.
Crespo scored Argentina's first goal of the 2006 World Cup in their opening match against the Ivory Coast. He also scored in the next game against Serbia and Montenegro (6–0) and the second round match against Mexico. However, Argentina's run was ended as they were knocked out by host nation Germany on penalties in the quarter-final.
Crespo's final appearances for Argentina came at 2007 Copa América. He scored twice in Argentina's 4–1 victory over the United States in their Group C opener, tying Diego Maradona's team scoring record. He then overtook Maradona in Argentina's second match, scoring a penalty kick against Colombia. However, he substituted immediately after converting the kick due to injury and missed the remainder of the tournament.
After the Copa América, Crespo did not receive any further call-ups to the national team and ended his international career with 35 goals in 64 matches, making him Argentina's third highest goalscorer of all-time, behind Gabriel Batistuta and Lionel Messi.
Hernán Crespo