The 26-year-old midfielder had been training in Coverciano, Italy, where the squad are on a pre-season camp.
Club doctors and Italian paramedics tried to revive Jarque without success.
His death comes two years after Sevilla defender Antonio Puerta, 22, died of heart failure after collapsing during a Spanish league game.
Jarque joined Espanyol at the age of 12, making his debut in 2002, and the Spaniard was handed the club captaincy this summer.
Jarque was a product of Espanyol's youth academy
"Tragedy struck Espanyol and the family of Dani Jarque this evening. The player died from a cardiac arrest," said a club statement.
"The doctor carried out CPR on the player and used a defibrillator, which showed that the arrest was non responsive.
"RCD Espanyol, broken with pain, wish to put themselves at the absolute disposition of the family of our captain Dani Jarque, to whom go our warmest thoughts."
Espanyol, who had been due to play Bologna on Sunday, have suspended their pre-season tour of Italy and will fly back to Barcelona.
"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," added club director German de la Cruz.
"The players are destroyed. One minute he was there with them, and the next he's gone. It's terrible."
The president of city neighbours Barcelona, Joan Laporta, offered his club's condolences.
"We are filled with extreme dismay at this tragic event which we deeply regret," he told the Barcelona club website.
"We are all in mourning. I want to send, on behalf of FC Barcelona, our deepest sympathies to RCD Espanyol for the painful loss of their captain Dani Jarque, and to his family."
As news of Jarque's death spread, tributes continued to pour in, with Real Madrid captain Raul also speaking of his shock.
"That such a young man, a great professional and sportsman, has suffered this has left us very upset," he said.
Other players who have died of heart failure include Cameroon midfielder Marc-Vivien Foe and Motherwell midfielder Phil O'Donnell.