After the attack, the woman was taken to a nearby hospital to be treated for serious injuries, and died early Tuesday morning.
A 52-year old man, originally from Dresden, has been arrested on suspicion of having committed the attack, according to police.
Police have confirmed that both attacker and victim were Germans who had been in a long-term relationship. The man had asked his ex-partner to meet him since it appeared that the relationship was on the point of collapse. But when they met he stabbed her several times and then fled the scene.
A string of bloody attacks have led to concerns in Germany about a rise in knife crime, and also given way to right-wing critics of Chancellor Angela Merkel, as some of the culprits have been teenage refugees.
In several of the attacks, the victim was apparently known to the attacker. On Tuesday, a teenage girl was stabbed to death in broad daylight by a teenage boy, suspected to be her ex-boyfriend, in the town of Viersen, North Rhine-Westphalia.