Essex Police said officers in Northern Ireland had arrested the man from Limavady in County Londonderry on suspicion of manslaughter and facilitating illegal entry into the UK.
He is due to be transported to Essex for questioning later.
A 40-year-old man who did not survive the journey has now been named as Meet Singh Kapoor from Kabul.
Police said that homicide inquiries will continue after a post-mortem examination carried out on Kapoor yesterday proved inconclusive.
The group included 13 children, one as young as one, and were found screaming and banging after arriving at Tilbury docks in Essex from Belgium.
They have now finished speaking to police and are being cared for by Home Office officials and are in the process of applying for asylum, Essex police said.
A Home Office spokesperson said: "We are continuing to provide expert support, along with the National Crime Agency, to the Essex police investigation into the discovery of 35 people in a container at the port of Tilbury on Saturday.
