The blast could be heard some 5km (3 miles) away and images from the scene showed the building reduced to a pile of rubble.
The head of the Veneto region, Luca Zaia, said the farmhouse was subject to an eviction order due to debts accrued by the three owners.
“This is a time for grieving,” said Interior Minister Matteo Piantedosi, who added that attempts had been made to evict the three siblings in the past.
“It was clear we were dealing with people who would resist in some way,” he said.
Mediators had been sent to speak to the siblings who had barricaded themselves into the house. When the Carabinieri arrived shortly after 03:00 (01:00 GMT), officials believe one of the siblings triggered the blast.
“Upon entering the house, we were confronted with an act of absolute madness,” provincial police commander Claudio Papagno told the Ansa news agency.
“A gas cylinder had been ignited, and the explosion directly hit our officers,” he said.
Petrol bombs were also found at the property, the interior minister said.
Those injured by the blast included 11 other members of the Carabinieri and well as three members of Italy’s state police and a firefighter, Ansa reported.
According to the Verona prosecutor, Raffaele Tito, the farmhouse was in a derelict state and had no electricity.
The prosecutor believed the blast had taken place on a floor above the entrance and told reporters it was a “premeditated and voluntary homicide”. Shortly before the explosion, he said officers had “heard a whistle, probably the gas cylinders being opened”.
“We all knew the situation was dire,” neighbours told Italian media, adding that the three had previously threatened to “blow themselves up” rather than leave the house.
Piantedosi said the explosion had left a “terrible, very painful and dramatic toll”.
Defence Minister Guido Crosetto joined other political leaders in paying tribute to the three men who had lost their lives in the service of their country.