The alleged cyber-attack against the Houston Astros is thought to be the first time a professional sports team has been hacked by another.
Trade discussions and proprietary statistics were reportedly targeted.
Major League Baseball has confirmed the investigation.
Baseballs officials told the Washington Post that the breach is being taken seriously in the sport, which is known for its data-heavy approach to managing players and schedules.
The Cardinals said they were co-operating with authorities but did not comment further. The Astros said they would not comment while the investigation was ongoing.
The Cardinals, which currently have the best record in baseball, are one of the most popular teams in the sport.
They have won the sport's championship, the World Series, 11 times, last earning the title in 2011. Only the New York Yankees have won more.
The Astros and the Cardinals were divisional rivals in the National League between 1994 and 2012.
The FBI is investigating the St Louis Cardinals on charges that the US baseball team hacked into the computers of a rival club to steal player data, the New York Times has reported.