Police were first contacted at 6-50am on Wednesday morning by a 34-year-old woman to say she had been seriously assaulted at an address in Comrie Crescent in the town.
She had suffered injuries including serious facial and neck injuries
She is currently being treated in hospital. Her injuries are not believed to be life threatening.
The attacker made off from the scene and was being hunted by officers.
At shortly before 6am today, police were contacted about a second assault which happened overnight at an address in Smith Street.
On police arrival officers found a 27-year-old man in the kitchen with serious facial injuries, and possible knife wounds.
A 21-year-old man from Burnley was arrested at the scene on suspicion of the attempted murder of both the 34-year-old woman and the 27-year-old man.
He is currently in custody.
Officers are appealing for anyone with information, in particular anyone who saw anything suspicious in the Comrie Crescent area between 2pm on Tuesday and 6-30am on Wednesday.
In relation to the second incident, police are also appealing for any witnesses around the Coal Clough Lane, Trafalgar Street or Smith Street areas from around midnight to 7am today.
Police want to speak to anyone who saw a man described as white, 5ft 7ins, bald, stocky build wearing a tan coloured coat, white trainers and grey jogging bottoms, possibly carrying a blue rucksack
Det. Insp. Vinnie De-Curtis said: “These assaults have left two people with extremely serious injuries and while we have made an arrest, our enquiries are very much continuing.
“We need to piece together exactly what has happened and to trace the movements of the man we have arrested between the first and second assaults so we can establish a precise chain of events.
“I would urge anyone who believes they can help to contact us.”
Anyone with information should contact police on 101 quoting logs 166 of March 1st or 0137 of March 2nd or Crimestoppers on 0800 555 111.