Swedish cabinet ministers do not usually have bodyguards 24 hours a day, though security has been tightened since the 2003 murder of foreign minister Anna Lindh.
Aftonbladet said in its online edition that police had uncovered plans for an attack against Bodström and his family, but provided no details of the nature of the threat.
The newspaper said police were informed of the threat “by informants in the underworld”, and the family had been under guard for a week.
Swedish intelligence agency Säpo, which provides security for members of the government, refused to comment on the report.
Bodström is married and has four children.
Lindh was killed in September 2003 when a man with a history of mental problems stabbed her repeatedly at a Stockholm department store where she was shopping without a bodyguard.