Officers found the woman at another address, where she was allegedly in possession of vehicle keys belonging to the homeowner.
Greater Manchester Police received a report of a suspected burglary at around 3am after a man returned to his home and discovered the front door had been secured on the latch from inside.
The man had left the door closed a short time earlier.
Information from neighbours suggested that a woman had been seen entering the property.
Officers from GMP's Bolton Neighbourhood Team identified a suspect and went to an address nearby.
Police said officers made repeated attempts to get the occupant to open the door before forcing entry.
A 47-year-old woman was found inside the property with vehicle keys believed to belong to the person who had reported the suspected burglary.
She was arrested on suspicion of burglary and remained in police custody for questioning at the time of GMP's statement.
Sergeant Zach Keneally, from Bolton Neighbourhood Team, said: "We understand these incidents can cause concern amongst those living in the area, but I hope this arrest provides some reassurance that we take these reports incredibly seriously and will always act on your concerns.
"No matter the time, your reports are vital to our mission to keeping GM a safe place for everyone.
"I encourage anyone who may have worries about criminality in their area to please report to us."
Anyone wishing to report suspicious activity can contact Greater Manchester Police on 101 or use the LiveChat service on the GMP website.
Information can also be passed anonymously to Crimestoppers on 0800 555 111.
In an emergency, call 999.
