Two first mates, one second mate and a chief engineer have been detained on allegations they failed to protect passengers, according to the Associated Press news agency.
The four crew members are also reportedly accused of abandoning the ship.
AP says prosecutors are considering whether to apply for a formal arrest warrant to allow for a longer period of investigation.
The ferry's captain and two other crew members have already been arrested on suspicion of negligence and abandoning people in need.
More top news
Showers in the north, perhaps turning heavy at times but becoming drier in the south towards the afternoon.
Police have stepped up their search for Younes Abouyaaqoub, believed to be at the centre of the investigation into the Las Ramblas attack.
The proportion of adults in families owning more than one property has surged, while the number of those with no property wealth also grew.