The CTK news agency said Dahlgren killed himself in a prison in Valdice northeast of Prague.
"I can confirm that we had a death by suicide in one of our prisons,"Petra Kucerova, spokeswoman for the Czech Prison Service, told AFP.
"I cannot give you more information as the case is under police investigation. But a prisoner has died," she added.
In May 2013, Dahlgren fatally slashed a man 29 times in his study before also stabbing the man's wife and their 23-year-old son to death at their home in Brno, eastern Czech Republic.
Following the frenzied assault, Dahlgren attacked the dead couple's 17-year-old son, striking him on the head with a stone as he returned home from school before stabbing him six times.
He then tried to burn the bodies of his victims inside the house.
Czech media said the dead woman was Dahlgren's cousin.
He got life in 2016 after the Brno court judge ruled that Dahlgren suffered from emotional instability, narcissism, paranoia and increased aggression.
Dahlgren claimed he had heard "a voice" telling him to attack his family.
Following the incident Dahlgren flew to Vienna and on to the United States where he was detained at a Washington airport the day after the killings.
In 2015, he became the first American to be extradited to the Czech Republic, an EU member of 10.6 million people.
Dahlgren's Facebook page said he was from Palo Alto, California, and that he had offered English lessons in Brno, the Czech Republic's second-largest city.