"The baggage and departure halls were evacuated, which has affected departing flights but not arrivals," police duty officer Roland Lindkvist said.
The halls were re-opened several hours later, after a bomb squad arrived from central Stockholm (about 100 kilometres or 60 miles away) and moved the bag to a safe area for examination.
"The bag in question belongs to an elderly lady and she is cooperating with us ... She says she doesn't know how the powder got on her bag," Lindkvist said.
Skavsta Airport is the fifth largest in the country and serves primarily low-cost and cargo carriers, handling around 2.5 million passengers a year.
This is the second airport bomb scare in Sweden in the last week.
Last Tuesday the police cordoned off an area at a Stockholm Arlanda airport car park at terminals 2 and 3 after security staff discovered the item in a rubbish bin outside the building.
"They found a small parcel in a bin and reacted to that, and made the assessment that a forensic team should look at it," Stockholm police control room officer Sven-Erik Olsson told the TT newswire.
Police were called to the scene at 4.41am and later took the suspicious item to a forensic lab for analysis. But by 9.30am they had reported that the item was not dangerous.