Five other senior managers were also targeted for house arrest or restrictions, including former top managers and current executives.
They face charges relating to transport safety violations and fraud.
The arrests were made at the request of the Genoa prosecutor, who is investigating the collapse.
Investigators previously accused the managers of knowing about, but failing to act on, defective soundproofing panels, design defects and unsactioned anchors.
Castellucci was the managing director of the company until January 2019. The Italian government is restructuring the company to place it under state control.
Prosecutors are investigating 70 people over the incident.
Genoa inaugurates new bridge, 2 years after tragedy — in pictures
Italy has opened the new bridge in the city of Genoa, almost two years after 43 people lost their lives when a viaduct collapsed. The bridge's architect described the day as a "mix of sorrow and pride."
Image: AFP/M. Medina
Tragedy strikes
The Morandi viaduct in the Italian port city of Genoa collapsed on August 14, 2018, causing the deaths of 43 people and injuring hundreds more. It was one of the biggest civil disasters in Italian history. Some of the pylons remained standing for almost a year until they were destroyed by controlled dynamite in June 2019 — to make way for a new bridge.
Image: Getty Images/AFP/M. Tacca
The man for the job
Star architect Renzo Piano was tasked with building a new bridge. Piano comes from the city and was originally given a deadline of April 2020 to complete construction of an ultra-safe new bridge. He told DW the inauguration day was a "mixture of sorrow and pride" for him.
Image: picture-alliance/dpa/A. Armellini
Construction overcomes setbacks
Despite bad weather during winter 2019 and the coronavirus pandemic both delaying pandemic, work rushed ahead and the new bridge was completed in near-record time. Over 1,000 workers were involved in the construction, which is named for St George. While the first bridge was described as representing all the shortcomings of Italy's infrastructure, it was hoped that this one would bring hope.
Image: AFP/M. Medina
Relatives of dead speak out
With the inauguration ceremony set for August 3, 2020, relatives of the dead chose not to attend. Some spoke out against the celebratory nature of the event given the tragedy associated with the loss of their loved ones in the collapse. Road company Autostrade is still under investigation regarding the collapse.
Image: picture-alliance/dpa/S. Arveda
Rain parts ahead of inauguration
Italian Prime Minister Giuseppe Conte was among those who spoke at a muted inauguration ceremony, before cutting a ribbon to officially open it. Conte acknowledged the tragedy of those who had died in the bridge collapse.
Image: Reuters/F. Lo Scalzo
National pride
The government hopes that the bridge will represent a sense of Italian achievement in a year that has seen the Italian economy and health service ravaged by the coronavirus pandemic. During the inauguration, aerobatic planes flew overhead streaming the colors of the Italian flag.
Image: picture-alliance/AP/L. Bruno
A bright future?
Despite the controversy, the bridge is cutting edge. Four maintenance robots run the length of the bridge constantly while a dehumidification system aims to limit corrosion. The high-tech structure may indicate a bright future for Genoa — but those who lost their lives will not be forgotten.