The investigation concerns reader comments made on the blog which according to Swedish Radio called for genocide of Palestinians.
A number of the comments under investigation were written in March and according to Swedish Radio remained on the blog until Thursday lunchtime.
Prosecutor Jörgen Lindberg told Swedish Radio that he was investigating a breach of the Act on Responsibility for Electronic Bulletin Boards. The law stipulates that the person in charge of a blog is responsible for removing comments that could constitute a breach of the law.
Bildt is not currently being treated as a suspect, but speaking to Aftonbladet, Lindberg said "we will see whether or not to declare him a suspect."
Lindberg is expected to make a decision in the autumn on whether to continue the investigation.
One of the comments being investigated called Palestinians 'spawn of Satan,' while another called them 'a bloody pack of murderers.' In one comment, a reader said: 'give us 24 hours and all Palestinians will be gone, and we'll have 100 percent of Israel.'
Chancellor of Justice Göran Lambertz, one of Sweden's most senior legal officials, is usually charged with prosecuting cases involving people's constitutional right to freedom of speech.
He ruled, however, that Bildt's blog was not covered by those sections of the constitution regarding free speech, meaning that police and prosecutors were able to take up the case.