The incident happened on Fiddlers Way off Sea View Road, East End, just before 7pm.
A combined team of police officers from the Eastern Districts, the Uniform Support Group, the Operational Support Unit and the Air Support Unit mounted an operation which resulted in the arrest of one suspect. The BB gun was also recovered, according to police.
The female who was struck by the pellet reported that she saw two males, one of whom with what appeared to be a gun under his arm, leaving the location. The police attended the area but no one was located and the woman was not injured.
Anyone with information on these incidents is asked to call 947 2220.