The collision took place in the St Mellons area of Cardiff on 4 March.
Passengers Darcy Ross and Eve Smith, and the driver Rafel Jeanne, died in the crash.
The offences for which the man has been arrested are not connected to the deadly crash itself, South Wales Police said.
But a detective said the arrest was connected to the same vehicle.
The man was arrested on suspicion of dangerous driving and driving while disqualified on the M4 at around 10pm on 3 March.
South Wales Police say he has been released on bail pending further enquiries.
Detective Chief Inspector Matt Davies of South Wales Police said: “The arrest was made as a result of evidence identified by officers investigating the fatal collision and involves the same vehicle.
“Our detailed investigation is continuing which will enable us to provide the facts of what happened during the early hours of Saturday 4 March.
“Our thoughts continue to be with the families and all those affected by this tragic incident.”