Security forces have launched a major search operation after the 25-year-old striker was abducted near Ciudad Victoria after leaving a party.
Local reporters said they saw soldiers and police officers in the streets of the Mexican city.
Alan Pulido plays for the Greek team Olympiakos and has made several appearances for Mexico’s national team.
Olympiakos said on its Twitter page: “At this difficult time, our thoughts and prayers are with Alan.”
Similar comments were published on social media websites by Alan Pulido’s teammates from the national squad.
Mexico has one of the world’s highest kidnapping rates, with government figures saying some 1,000 people are abducted every year.
Others argue that the true figure could be almost 10 times as high.
Local media reports said Alan Pulido had been leaving a party with his girlfriend in the early hours of May 29 when their car was surrounded by several trucks.
Six masked men reportedly took the striker away “by force” while Alan Pulido’s girlfriend was left unharmed in the car park where the incident took place.
Tamaulipas is one of Mexico’s most violent states, and Mexico recently deployed more security forces to tackle cartels operating in the area.
Dozens of people have been killed in recent weeks in the border state, which is criss-crossed by drug-smuggling routes to the US.
Alan Pulido joined Olympiakos in July 2015 and finished the season with six goals in 15 games.
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