The man was reported dead at the Yarl's Wood centre earlier.
A Home Office spokesman said Bedfordshire Police had been informed and a full inquiry would be carried out by the Prisons and Probation Ombudsman.
Sally Chidzoy, BBC Look East Home Affairs Correspondent, said a source at the centre told her the man died after drinking an energy drink.
She said: "My source says the man who died had been arrested with his wife and child over an alleged breach of visa regulations at an airport. They are believed to have travelled from the Indian subcontinent.
"I have been told he was staying at the Hummingbird wing. In the morning he was having breakfast with his wife, and was laughing and joking.
"He was given an energy drink and shortly after collapsed and died, I am told."
A Home Office spokesman added: "Our thoughts are with the family at this very sad time."
The spokesman could not comment on claims that he died after drinking an energy drink.
A detainee has died at an immigration removal centre in Bedfordshire, the Home Office has confirmed.