The Hausers have said that they would prefer a less rigid chemotherapy treatment combined with other alternative treatments.
The family is Roman Catholic and believes in the "do no harm" philosophy of the Nemenhah Band, a Missouri-based religious group that believes in natural healing methods.
The warrant for deprivation of parental rights will ensure extradition to Minnesota if she is apprehended, according to police.
Authorities said the fugitives do not own a car and don't believe they could have left Sleepy Eye without help. They say they are following "any and all leads" and have been receiving tips from across the country.
Hoffman said that authorities do not have a specific vehicle they are looking for.
Authorities had said they believe Colleen and Daniel could be with a Massachusetts' man who fled his own chemotherapy treatment in 1994, according to The Associated Press.
Billy Joe Best was 16 when he fled to Houston to escape treatment for Hodgkin's disease, according to the AP. He returned home only after his parents promised that they would not force him to have the treatments. Best claims to have beaten cancer by using natural remedies.
Calls made by ABC News to the Best residence in East Bridgewater, Mass., were not immediately returned.
But late Wednesday the AP reported that Best denied he was with Hauser and her son, saying that he had not spoken to them since they fled.
Colleen Hauser's husband, Anthony, said that he believes his wife saw X-rays of Daniel that made her scared and prompted her to flee, missing a court appearance Tuesday.
Hauser has been cooperating with police, but Hoffman declined to speculate on the "sincerity of the information."
Daniel's name has been added to the database of the national Missing and Exploited Children's Network, said Hoffman, who hopes the move will help spot the teen if he attempts to cross a border.
The Associated Press contributed to this report. t