Officers forced entry into the house on Turnstead Drive in Cleckheaton at 4.20pm on Monday, May 11 after concerns were raised for the welfare of two people inside.
A woman in her 30s was found inside with a minor stab wound to her leg.
A man in his 40s received minor injuries.
Police arrested a 30-year-old man from the scene on suspicion of false imprisonment and assault.
He remains in police custody.
DI Andrew Lockwood of Kirklees CID, said: “We are continuing to investigate this incident this morning and are holding a man in custody.
“Due to the nature of the reports we received, armed officers were deployed and specialist police tactics were used by officers to enter the property.
“We do currently believe this was an isolated, targeted offence and we are working to support the victims as our enquiries continue.
“Reassurance patrols will be ongoing in the local area today by Batley and Spen Neighbourhood Policing Team officers.”
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