Michael John Anderson is accused of shooting Katherine Ann Olson in the back at his home in suburban Savage, according to the criminal complaint filed in Scott County District Court.
Bail was set at $1 million.
"At this point, we don't know a whole lot about our suspect," Savage police captain David Meulkin told CBS News Early Show co-anchor Harry Smith. "We have had some minor juvenile contacts with him, nothing serious, and certainly nothing violent and nothing that would indicate this."
Olson had gone to Anderson's home Thursday to inquire about a baby-sitting job she had seen advertised on the popular Internet bulletin board, authorities said.
"I think her success with getting employment through Craigslist gave her some more confidence too," Meulkin told Smith. "And people really need to be aware of making contact with strangers."
"Take it with a little bit more caution," Katherine's sister, Sarah Richter, told CBS News correspondent Dean Reynolds, referring to the use of Craigslist. "People are really good people except for a few bad apples."
A spokesman for Craigslist said if a link is confirmed, it would be the first murder ever tied to Craigslist in its 12-year existence and over 450 million classified ads.
Authorities said Olson's blood was found in Anderson's home and a gun was found in his bedroom. A neighbor saw Olson's car sitting in front of Anderson's house for more than two hours Thursday, the complaint said.
The body of the 24-year-old Minneapolis woman was found Friday night in the trunk of her car, which was abandoned in a park about five blocks from Anderson's home. Olson's purse and a bag containing bloody towels, one of which bore Anderson's name, were found in trash nearby.
Anderson has been in the Scott County Jail since his arrest late Friday.
Cell phone records indicated he talked with Olson on Thursday morning, the court documents said. Anderson also said he had not used Craigslist since January, although the e-mail address in the ad matched his address. He told police his mother and three friends had access to the account.
When confronted with evidence, Anderson admitted he was present during Olson's slaying but said the killing was committed by a friend of his who "thought it would be funny," according to the complaint.
"She was going to set the world on fire, and that's the grief that we feel," Nancy Olson, Catherine's mother, told Reynolds. "It's not just for us. It's for all these other people that she would have touched."