Two men died at the scene, while the third remains in hospital in a serious but stable condition.
Bedfordshire Police said the man, in his 30s, had been arrested on suspicion of two counts of murder and one of attempted murder.
Temporary Det Supt Carl Foster, from the Bedfordshire, Cambridgeshire and Hertfordshire Major Crime Unit, said: "This was a shocking incident which has occurred in a busy area of Houghton Regis and has no doubt caused great concern to the local community.
"We have a dedicated team working on this investigation and are carrying out a range of inquiries in order to bring those responsible to justice."
He said there would be an increased police presence in the town over the coming days.
Earlier, a group of the town's councillors wrote a letter to the force's chief constable highlighting "the reality of knife crime on our streets and in our school so lives can be saved" and requesting a larger police presence generally.
"The devastation has a ripple effect on everyone involved and the wider community, who sadly have to live in fear in case of repercussions," the councillors said.
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