Police were called at 22:30 BST on Tuesday to a travellers' site at Toddbury Farm in Slapton Road, Little Billington, near Leighton Buzzard.
A man, aged 43, was taken to hospital where he was pronounced dead.
Police confirmed a man aged 24 and a woman, 42, have been arrested on suspicion of murder. Both remain in custody.
The victim, who officers say lived at the site, has not yet been named.
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Det Insp Alan Page from the Major Crime Unit said: "Though we appreciate the traumatic effect that an incident such as this will have on the traveller and wider community, we would urge members of the public not to be alarmed.
"We are conducting a full and thorough investigation into the events of last night and will maintain a visible, heightened presence in the area for reassurance and intelligence-gathering processes."
A post-mortem examination on the deceased man is expected to take place on Thursday.
Two people have been arrested on suspicion of murder following the death of a man in Bedfordshire.