A preliminary inquiry found that gondolier Stefano Pizzaggia had consumed cocaine and marijuana, said the reports citing police sources. He risks charges of manslaughter.
The driver of the vaporetto involved in the collision and those of two other vaporetti are also part of the investigation.
The accident happened on Saturday on Venice's Grand Canal near the city's famous Rialto Bridge as the public transport waterbus manoeuvred toward a stop.
The 50-year-old German man, identified as a criminal law professor from Munich, his wife and three children and the gondolier all fell into the water in the accident. Other gondoliers rushed to the rescue, taking them to the bank.
The waterbus reportedly crushed the German man, named as Joachim Reinhard Vogel, against the gondola.
His three-year-old daughter suffered a head injury and was taken to hospital in nearby Padua.
As a sign of mourning the 425 gondolas normally in service suspended their activity on Saturday.