Authorities arrived on the scene after being informed that "a person with a knife wanted to kill someone," Oslo police said on Twitter.
"When they arrived, they saw a person was preparing to stab a child with a knife. Police shot her" said another Tweet, without specifying the relationship between the woman and child.
The woman was hospitalised, and her and the child's condition were not immediately known.
Norwegian police, who are not usually armed, have been temporarily carrying more firearms due to increased jihadist threats against authorities.
However, they drew their weapons only 42 times in 2014 and fired them only twice.
Only two people have been killed in police shootings in Norway over the last 12 years.