The failed asylum-seeker, who has not been named, was discovered by staff in the family unit and was rushed to hospital. He died soon after arriving.
Anti-deportation campaigners said the man was a 35-year-old Angolan who had been living in Leeds with his son before they were taken to the Yarl's Wood Immigration Removal Centre, in Bedfordshire.
The death at the centre, built to house 900 detainees, comes at a time when 30 Ugandan women being held there are on hunger strike. Anti-deportation campaigners are organising a demonstration outside the centre, run by GSL Ltd, a private company, on Saturday.
Emma Ginn, of the National Coalition of Anti-Deportation Campaigns, said: "If this man was frightened enough to kill himself what he was facing must be pretty awful. Assaults, disturbances, hunger strikes and suicides have been a not infrequent feature in the immigration detention and removal process."
Yarl's Wood was the scene of a major riot soon after it opened in February 2002, when it suffered extensive fire damage, thought to have cost £38m. In August this year a report for the Chief Inspector of Prisons, Anne Owers, found that Yarl's Wood detainees were twice as likely to report feeling unsafe as those in other centres.
A Home Office spokesman said that they could not comment on the case but the prisons and probation service ombudsman has begun an inquiry.
"The Immigration Service takes very seriously their responsibilities towards minors and we work very closely with social services to ensure the welfare and safety of the children."
Ms Ginn said representatives of the Angolan community in Leeds had been contacted to try to find someone to care for the dad man's son.
Yarl's Wood was opened in late 2001 by Group 4 at a cost of £90m as as part of a policy to remove 30,000 failed asylum-seekers and illegal immigrants.