Jarque had trained in the morning but collapsed in his hotel room in Coverciano while talking to his girlfriend on the telephone in the early evening, Spanish media reports said.
"The Espanyol player died due to a systolic heart failure," the club said in a statement.
"[Club doctor] Doctor Cervera tried CPR on the player and used a defibrillator but said it was not possible to resuscitate.
"Within minutes, the first emergency ambulances arrived from Florence, and tried their defibrillators but again were unable to resuscitate."
Medical services tried to revive Jarque for an hour before pronouncing the player dead, the club said.
"Espanyol are distraught and wish to put themselves at the complete disposal of our captain's family," they added. Club director German de la Cruz told radio station RAC1: "It's inexplicable. It's horrific.
"We are returning to Barcelona on Sunday but we can't come back with the coffin because they have to do an autopsy to confirm the cause of death.
"The players are destroyed. One minute he was there with them, and the next he's gone. It's terrible."
The club had been due to play friendlies against Bologna and Livorno in the coming days, on their Italian tour.
Jarque came up through the youth ranks at Espanyol, helping them win the King's Cup in 2006 and to reach the UEFA Cup final in 2007, and had just been made captain of the club for the new season.
Jarque's death comes nearly two years after that of Sevilla midfielder Antonio Puerta who died on August 28, 2007, three days after collapsing during a Primera Liga match against Getafe.