Gun shots were fired at a property in Devon Road where a mother and her children were going to bed last night.
Police confirmed the shots were fired just after 9pm but no one was hurt.
Voices were heard before the shotgun was fired, and then two male offenders made off on a motorcycle towards Crawley Green Road.
Det Insp Iain Morgan said he believes the shooting was deliberately targeted.
He said: “I am appealing to anyone who has information about this offence or who was in or near the area at the time and recalls hearing or seeing the motorcycles or the offenders before or after the offence. I firmly believe this offence was aimed at specific people living at the location and would reiterate very strongly that Bedfordshire Police does not tolerate the use of violence and firearms. If you have information about this please contact the police in confidence.”
The incident is not thought to be related to the wider ongoing gun crime in Luton and is being dealt with separately.
Beds Police have so far this year arrested 63 people, executed 55 warrants, recovered 27 firearms, carried out 231 overt patrol stop-checks and charged four people with firearm/weapon offences.
A further 12 people are currently on bail for similar offences.
Anyone with information relating to this incident can contact Bedfordshire Police on 101, or text information to 07786 200011.