At least two people are believed to have been be injured during the incident in Ramersdorf, near Munich.
After a fierce dispute with his ex-partner, the 29-year-old unemployed man took the woman's four children and stole her car before crashing into two pedestrians.
The pedestrians, two men, were seriously injured and were taken to hospital following the incident. The children were uninjured during the incident, police said.
Police officer Carsten Neubert said the suspect had argued with his 26-year-old ex-girlfriend in her apartment, which resulted in him hitting her.
The woman escaped from the flat and had sought protection from a neighbour before her ex took her car keys and her four children, who are aged between 14 months and five-years-old.
He bundled the children into the car and drove off - supposedly to look for the mother, police said.
According to the police, the man, who is being hunted by officers, is not the father of the children.